Preheat your oven to 450°F (230°C) and line a baking sheet with parchment paper.
In a large bowl, combine the flour, baking powder, salt, garlic powder, and onion powder.
Add the cold cubed butter to the dry ingredients. Use a pastry cutter or your fingers to work the butter into the flour until the mixture resembles coarse crumbs.
Stir in the shredded cheddar cheese and diced ham.
Pour in the buttermilk and stir until the dough comes together. Be careful not to overmix, as this can result in dense biscuits.
Turn the dough out onto a lightly floured surface and gently knead it a few times to bring it together. Pat it into a rectangle about 1-inch thick.
Use a biscuit cutter or a glass to cut out rounds of dough and place them onto the prepared baking sheet.
Brush the tops of the biscuits with melted butter.
Bake for 10-12 minutes or until the biscuits are golden brown and cooked through.
Serve warm, and enjoy!