Make the puffs: Preheat the oven to 375 degrees F.
In a sifter, combine the flour and cocoa powder. Sift onto a large piece of waxed paper and set aside until needed.
Heat the water, 4 tablespoons butter, and 1 tablespoon sugar in a 3-quart saucepan over medium-high heat. When hot, stir to dissolve the sugar. Bring to a boil. Remove from the heat and add the sifted dry ingredients. Use a wooden spoon to stir until the mixture comes together in a ball-like shape (it should be a bit like putty at this point). Add the eggs, one at a time, stirring energetically and thoroughly incorporating each egg before adding another. Divide the dough in level tablespoons (approximately 1/2-ounce per puff) onto 2 nonstick baking sheets, 12 evenly spaced portions per sheet. Place the baking sheets on the top and center racks of the preheated oven and bake for 20 minutes, rotating the sheets from top to center halfway through the baking time (at that time also turn each sheet 180 degrees). Remove the puffs from the oven and cool to room temperature.
Make the Chocolate Caramel Ganache: Place the chopped semisweet and unsweetened chocolate in a 4-quart bowl and set aside. Heat the heavy cream and 2 tablespoons butter in a 1 1/2 quart saucepan over medium heat. Bring to a simmer, then lower the heat to keep the cream hot, but not simmering until needed. Combine 1/2 cup sugar and the lemon juice in a 3-quart saucepan. Stir with a whisk to combine (the sugar will resemble moist sand). Caramelize the sugar for 7 to 8 minutes over medium-high heat, stirring constantly with a whisk to break up any lumps (the sugar will first turn clear as it liquefies, then, light brown as it caramelizes). Remove the saucepan from the heat. Carefully pour about 1/3 of the hot cream into the caramelized sugar. Use a whisk to stir the caramel until it stops bubbling. Add the remaining cream and stir until smooth. Immediately pour the hot caramel over the chopped chocolate and allow to stand for 5 minutes before stirring with a whisk until very smooth. Refrigerate the ganache until just slightly firm but not hard (if the ganache is too firm, it will be difficult to pipe).
Using a sharp paring knife, cut each puff in half horizontally. Transfer the chilled ganache to a pastry bag fitted with a large star tip. Pipe about 1 heaping tablespoon (approximately 1-ounce) of ganache onto the bottom half of each puff, then place the top half of the puff onto each portion of ganache. Serve immediately, or store in a tightly sealed plastic container at room temperature for 12 to 24 hours.