In a large bowl, combine the batter, cornmeal and half-and-half. In another large bowl, beat the cream cheese, confectioners sugar and lemon peel until fluffy. Beat in the lemon juice.
Using an electric mixer, beat the heavy cream until soft peaks form. Fold into the cream cheese mixture and refrigerate.
Preheat a nonstick skillet over medium-high heat. Grease the pan with some butter. Add 2 tablespoons of the cornmeal batter and, tilting and rotating the pan, form a thin crepe. Cook until golden, 1 minute; flip and cook for about 15 seconds. Repeat with the remaining cornmeal batter and butter.
In a heavy saucepan, bring the granulated sugar and 1/2 cup water to a boil over medium-high heat. Cook, undisturbed, until golden, about 10 minutes. Stir in the apricots and 1/4 cup water.
Meanwhile, working in batches, arrange the crepes on a work surface and spread some of the cream cheese mixture on each one. Fold the crepes in half, then fold in half again to form a fan. Top with the apricot-caramel sauce and dust with confectioners sugar.