Arrange a rack in the middle of the oven and heat to 350°F. Coat a 9x13-inch baking dish with butter or cooking spray; set aside.

Place the 2 ½ pounds pitted and halved sweet cherries, ½ cup granulated sugar, 1 tablespoon lemon juice, and 1 tablespoon cornstarch in a large bowl and stir to combine; set aside.

Place 3 cups all-purpose flour, ¾ cup granulated sugar, ½ teaspoon baking powder, and ½ teaspoon kosher salt in a food processor fitted with the blade attachment and pulse to combine.

Add 2 large egg yolks, 2 teaspoons almond extract, and 2 sticks cubed cold unsalted butter. Pulse in 5-second intervals just until the dough comes together, about 1 minute total. The dough will be soft and slightly crumbly.

Transfer ⅔ of the dough to the pan. Use a fork or your fingers to press the dough into the bottom of the prepared pan.

Add the cherry mixture and spread into an even layer.

Scoop about a tablespoon of the remaining dough, press it together in the palm of your hands, and place on top of the cherries. Repeat with the remaining dough, evenly spacing it over the top of the fruit. (The cherries will not be completely covered.)

Brush the dough with 1 tablespoon melted unsalted butter and sprinkle with 1 tablespoon demarara sugar.

Bake until the top is golden and the cherries are bubbling, 35 to 40 minutes.

Cool completely in the pan before cutting into 12 bars.