Preheat oven to 400º and butter a 9×13-inch baking dish.
Spread peach slices evenly along bottom of baking dish. Combine sugar, cornstarch, salt, and cinnamon in a small bowl and mix well. Spoon sugar mixture evenly over peaches. Sprinkle lemon juice and almond extract on top. Stir to distribute. Scatter butter cubes over the top. Place in oven and bake for 15 minutes.
While peach filling is baking, stir together flour and cheese in a large bowl. Combine melted butter and buttermilk in a small bowl and slowly pour into flour mixture, stirring gently with a fork. Mix just until a dough is formed.
Remove baking dish from oven once it has baked for 15 minutes and stir gently to make sure sugar has dissolved.
Drop dough by rounded tablespoons on top of filling. Return to oven and bake for about 20 minutes, until biscuit topping is golden brown and firm.
Serve warm with ice cream.