Grate the Asiago and Parmesan cheese. Add both cheeses to a food processor.
Add all the spices into the food processor with the cheese. Pulse until everything is well mixed and the cheese is a fine texture.
Place the cheese mixture into a bowl. Add a cup of olive oil and mix. Add more if needed.
Cover the bowl and chill for at least 24 hours to let the flavors meld.
Serve chilled or at room temperature on unsalted/lightly salted crackers. Can also be served with toast and fresh tomatoes or used to flavor roasted vegetables. Keep the unused spread in the refrigerator for up to three weeks.
