Place Parmesan and Asiago cheese chunks into a food processor; process about 10 seconds or until cheese breaks into small granules.
Add garlic, pepper, basil, green onions, pepper flakes, and olive oil to the bowl of a food processor; process until mixed in.
Transfer the topping to a sealed container and refrigerate for up to a week. Bring to room temperature before serving.
Yields approximately 3 1/2 cups.
Parmesan-Asiago Spread Recipe: https://whatscookingamerica.net/appetizers/parmesanasiagotopping.htm