Preheat the oven to 350 degrees F. Grease an 8-inch-round baking pan, line with parchment paper, then grease and flour the pan. In the bowl of an electric mixer fitted with the paddle attachment, cream the butter and sugar on medium speed for 3 to 5 minutes, until light and fluffy. Scrape down the sides with a rubber spatula. Add the eggs, one at a time, the molasses and the 2 teaspoons lemon zest and mix until combined. (The batter may look curdled.)
Sift together the flour, ground ginger, baking soda and salt. With the mixer on low, slowly add the dry ingredients, alternating with the milk, scraping down the sides. Mix until smooth. With a rubber spatula, fold in the 1/3 cup crystallized ginger.
Pour the batter into the prepared pan, smooth the top and bake for 30 to 35 minutes, until a toothpick just comes out clean. Don't overbake it! Cool in the pan for 30 minutes, turn out onto a baking rack and cool completely. Spread the top with whipped cream and sprinkle with crystallized ginger and grated lemon zest.
For the whipped cream:
Place the cream, confectioners' sugar, granulated sugar, creme fraiche and vanilla in the bowl of an electric mixer fitted with the whisk attachment. Beat on high speed, until it forms soft peaks. Refrigerate up to 4 hours before serving.
Make it ahead: Prepare the cake. Wrap tightly and refrigerate for up to 1 day. Garnish with whipped cream, ginger and lemon zest. Ina says,"If you add just a little creme fraiche to stabilize the whipped cream, you can make it a few hours ahead."