To assemble the Poire Belle Helene, place a scoop of chocolate ice cream at the bottom use a sundae glass. Drizzle the chocolate sauce over the ice cream then place a pear on top. Drizzle more chocolate sauce on top of the pear, and top it with whipped cream and another drizzle of sauce.
Pour the water, sugar, lemon zest, and lemon juice into a non-reactive 4-quart heavy-bottomed saucepan and place over medium-high heat. Using a sharp knife, slice the vanilla beans in half lengthwise. Separate the seeds from the skins by scraping the blade of the knife along the inside. Add the seeds and skins to the mixture and continue heating.
Peel and core the pears but do not halve them. Coring the pears from the bottom will encourage the poaching liquid to seep inside the pear and help it cook evenly inside and out. Add the pears to the lemon mixture and bring to a boil. When it reaches a boil, reduce the heat to a simmer and let cook for about 1 hour. Do not overcook the pears; they should be soft enough to pierce easily with a wooden skewer or toothpick.
In order to keep the pears immersed in the liquid and help them to poach evenly, you must make a parchment paper lid to cover them. To make the lid, cut a round disk from a sheet of parchment paper that is slightly smaller than the diameter of your pan. Place the paper lid directly on top of the pears and poaching liquid. When the pears are fully poached, pour them and the poaching liquid into a clean container. You will need 1 whole pear for each serving.
Heat the milk and chopped chocolate together in a 2-quart heavy-bottomed saucepan (this will keep the milk from burning) over medium-high heat until bubbles form around the edge of the pan. While the milk is heating, combine the sugar and egg yolks and whisk until thoroughly incorporated and thick. Temper the egg mixture by pouring about half of the hot milk into it and whisk well. Now pour the tempered egg mixture into the remaining hot milk and chocolate. Cook over medium-high heat until slightly thickened, stirring constantly with a rubber spatula. The mixture has finished cooking when it is thick enough to coat the back of the spatula, about 3 to 5 minutes. If you want to reduce the cooling time, you can cool the chocolate ice cream base over an ice bath. When the mixture is cool, spin it according to the type of ice cream machine you are using. The ice cream is ready when it is creamy and smooth, like the consistency of soft-serve ice cream. Place the ice cream in an airtight container and store in the freezer until ready to use.
Pour the milk into a 2-quart heavy-bottomed saucepan, place over medium-high heat, and bring to a boil. When it boils, remove the milk from the heat and make a ganache by adding the chopped chocolate. Whisk well, stirring into the edge of the saucepan to combine. The ganache should be homogenous and smooth. Set the ganache aside. In a 1-quart heavy-bottomed saucepan, combine the heavy cream, butter, and sugar. Place the saucepan over medium-high heat and bring to a boil, stirring occasionally. The butter should be completely melted and the sugar completely dissolved. Once the mixture has come to a boil, pour the cream into the warm ganache.
Place the sauce over medium-high heat and bring to a boil, stirring constantly with a whisk. As the chocolate sauce cooks, it will begin to thicken slightly. When it reaches a boil, remove it from the heat and pour it into a clean, dry bowl. Cover by placing plastic wrap directly on top of the sauce to prevent a skin from forming. Let the chocolate sauce cool to room temperature before storing in the refrigerator. When cold, the chocolate sauce will become thick enough to be scooped with a spoon.
For the pears: The pears can stay in the poaching liquid for up to 3 days, each day they will become more flavorful and colorful. A few hours before serving, remove the pears from the liquid and drain them on a wire rack placed over a parchment paper-covered sheet pan. For the sauce: This sauce can be reheated whenever needed. If using a microwave, simply place the chocolate sauce in a microwaveable bowl and heat it at medium-high power in 30-second intervals until it becomes liquid. On the stovetop, place in a heavy-bottomed saucepan over medium heat and stir occasionally until it becomes liquid. If you store it in a squeeze bottle, you can easily drizzle it over a dessert or decorate a plate. It will keep in the refrigerator for up to 3 weeks. It can also be frozen for up to 2 months if stored in an airtight container. Thaw in the refrigerator and heat as described above until liquid. For the ice cream: Use the following method to tell if it is finished: Quickly dip the spatula into the hot mixture and hold it horizontally in front of you. With the tip of your finger, wipe a clean line down the center of the spatula. If the mixture holds and does not fill in the line, it is ready to be removed from the heat. If the line fills with liquid, the mixture must be cooked a little longer. Repeat the test every 30 seconds until ready. At no time should the mixture begin to boil. If you see bubbles begin to form around the edge of the pan, remove the pan from the heat and whisk the mixture thoroughly to cool it down. Once the mixture has finished cooking, pour it into a clean bowl and set aside to cool.