FOR THE ICE CREAM: Transfer the ice cream to a medium bowl and, using a rubber spatula, fold in the ground espresso until incorporated. Press a sheet of plastic wrap flush against the ice cream to prevent freezer burn and return it to the freezer. (The ice cream can be prepared up to 24 hours ahead.).
FOR THE CAKES: Lightly coat eight 4-ounce ramekins with butter. dust with sugar, tapping out any excess, and set aside.
Melt the bittersweet and unsweetened chocolates and 10 tablespoons butter in a medium bowl over a medium saucepan of simmering water, stirring occasionally, until the chocolate mixture is smooth. In a large bowl, whisk the 1 1/2 cups sugar and cornstarch together. Add the chocolate mixture and stir to combine. Add the eggs, egg yolks, and Grand Marnier and whisk until fully combined. Scoop 1/2 cup of the batter into each of the prepared ramekins. (The ramekins can be covered tightly with plastic wrap and refrigerated for up to 24 hours.).
Adjust an oven rack to the upper-middle position and heat the oven to 375 degrees. Place the filled ramekins on a rimmed baking sheet and bake until the tops of the cakes are set, have formed shiny crusts, and are beginning to crack, 16 to 20 minutes.
Transfer the ramekins to a wire rack and cool slightly, about 2 minutes. Run a paring knife around the edge of each cake. Using a towel to protect your hand from the hot ramekins, invert each cake onto a small plate, then immediately invert again right-side up onto 8 individual plates. Sift confectioners' sugar over each cake and the area of the plate where the ice cream will be placed. Remove the ice cream from the freezer and scoop a portion on top of the confectioners' sugar, next to the cake. Serve immediately.