Make the cheese: Line a large fine sieve with 3 layers of cheesecloth, and set over a large bowl. Heat buttermilk in a medium saucepan over medium-low heat, without stirring, until clear liquid separates from milk at edges or a candy thermometer clipped to the edge of the pan registers 95 degrees. Reduce heat to low; cook until thermometer registers 100 degrees. Remove from heat; let stand 3 minutes. Pour into sieve; cover bowl loosely with plastic wrap. Refrigerate until thick and creamy, about 3 hours (up to overnight). Before serving, stir in confectioners' sugar.
Make the crepes: Whisk flour, cornmeal, baking soda, salt, and nutmeg in a bowl. Whisk egg, egg white, milk, buttermilk, honey, and oil in another bowl; gradually add to flour mixture, whisking until smooth. Transfer to an airtight container; refrigerate 30 minutes.
Coat an 8-inch crepe pan with cooking spray; heat over medium heat. Remove from heat; pour in 2 1/2 tablespoons batter, swirling to coat. Reduce heat to medium-low. Cook, flipping once, until edges are golden and center is dry, 45 to 60 seconds per side. Repeat with remaining batter.
Toss together berries and cassis. Let stand 15 minutes, tossing often. Divide crepes among plates. Spread each with 1/4cup cheese. Sprinkle with berries; drizzle with juice from bowl. Dust with sugar.