Preheat the oven to 400 degrees F (200 degrees C).
Combine flour, baking powder, salt, baking soda, and garlic powder in a bowl. Whisk to combine.
Dice the cold butter up into chunks, and cut it into the dry mixture with your fingers, a fork, or a pastry cutter, until the mixture resembles coarse sand, and butter is well blended in. Stir in cheese and ham, gently stirring to evenly coat all the cheese and ham pieces with the flour mixture.
Use a fork and stir in 1 cup buttermilk. If the mixture is still dry, add a little more liquid at a time until the dough just comes together (it should be a little bit sticky, but not "wet").
Shape dough into a ball by hand, handling the dough gently. Then pat the dough out on a lightly floured surface to 1/2- to 3/4-inch thickness. Use a small biscuit cutter to cut 12 to 15 biscuits out, and arrange them on a baking sheet with sides just barely touching.
Bake in the preheated oven until just golden brown around the edges/tops/bottoms and cooked through in the center, 12 to 15 minutes.
Cool briefly on the baking sheet before moving to a platter or cooling rack. Best served warm!