Add flour and sliced butter to a mixing bowl. Using a pastry cutter, 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 dough into a ball. Cover the dough with plastic wrap and refrigerate for 1 hour.

Preheat oven to 375 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.

On a piece of flour-dusted parchment paper, roll dough into a roughly 12-inch. Leave the dough on the parchment paper and transfer to a baking sheet.

Spoon fruit onto the dough and spread evenly, leaving a 2-inch border along the perimeter. Fold dough edges over, crimping and pleating as needed. Brush the beaten egg over the dough and sprinkle with 1-tbsp. brown sugar.

Bake on center rack until golden brown and bubbly, about 45 minutes. Transfer to a cooling rack and cool for at least 20 minutes before slicing. Serve with ice cream or whipped cream, if desired.