Preheat oven to 400.
In a food processor add flour, baking powder, baking soda, salt, and sugar.
Pulse to combine. Add the cold butter, process until well combined. Add to a large bowl.
Add the buttermilk and beer. Mix with a fork until just combined.
Add to a well-floured flat surface, pat into a rectangle. Using a cold rolling pin gently roll into a large rectangle, about 3/4 inch in thickness, using as few strokes as possible.
In a small bowl stir together the softened butter, garlic, garlic powder and pinch of salt.
Spread the dough with the butter mixture (reserving 2 tablespoons), sprinkle with grated cheese.
Starting at the long end, roll into a tight log. Cut 2-inch rounds, place in a baking dish.
Melt the remaining 2 tablespoons garlic butter, brush the top of the rolls with the melted butter.
Bake at 400 for 14 to 16 minutes or until the tops are golden brown.
Serve warm.