Mix milk, flour, eggs, melted butter, 2 tablespoons white sugar, and salt together in a bowl. Cover batter with plastic wrap and refrigerate 8 hours to overnight. Thin batter with water, mixing well, if it becomes too thick.

Mix cottage cheese, cream cheese, confectioner's sugar, and vanilla extract together until well blended; the filling will not be smooth.

Place blueberries in a saucepan and cover with water. Add 1/2 cup sugar and cook over medium-high heat until mixture starts to boil. Reduce heat a bit; simmer for 3 to 5 minutes to allow berries to release juice. Add more sugar if desired; simmer for 3 to 5 minutes more.

Mix cornstarch with cold water in a bowl until dissolved. Remove berry mixture from heat and slowly pour in cornstarch mixture. Stir constantly until thickened.

Melt 1/4 teaspoon butter in a skillet over medium heat. Pour batter into the skillet to make an 8-inch pancake. Cook until lightly browned, 2 to 3 minutes. Flip and brown the other side, about 1 minute more. Transfer to a plate to cool slightly. Add filling to the center of the pancake, roll up, and transfer to another plate. Top with berries. Repeat cooking, filling, and topping with the remaining batter.