Place flour and cold sliced butter into a mixing bowl. Using a pastry blender, cut the butter into the flour until the mixture is the size of small peas.
Add cottage cheese and mix with a spoon until combined. Using your hands, shape into a ball.
Cover dough with plastic wrap and chill for 1 hour.
Preheat oven to 400 degrees.
Place peaches and blueberries in a large bowl. Add ¼ cup brown sugar, cornstarch, and almond extract. Gently toss to coat the fruit. Set aside.
Roll dough to a 12-inch circle on a piece of flour-dusted parchment paper. Leave the dough on the parchment paper and transfer to a baking sheet.
Spoon fruit mixture onto dough circle, and spread toward edges, leaving about 2-inches all around without fruit.
Fold dough edges over, crimping and pleating edges as needed all around.
Brush the beaten egg over crust edges and spinkle with the 1-tbsp. brown sugar.
Bake on center rack of the preheated oven for about 45 minutes or until browned.
Remove to a cooling rack and cool before slicing.