Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
Whisk together the flour, baking powder, salt and baking soda in a large bowl. Add the butter and use your hands to work it into the flour mixture until it resembles small pebbles. Add the Cheddar and toss lightly.
Add the buttermilk and ale and stir in with a wooden spoon just to combine. Using a 1/4 cup measure, scoop the dough onto the baking sheet, leaving about 1 1/2 inches between biscuits. Bake until golden brown, 20 to 25 minutes. Serve warm.