Heat oven to 375 degrees.
Place 2 cups onion in a bowl. Shred Jack and cheddar cheeses.
Combine shredded cheeses, cream cheese, mayonnaise, thyme and remaining 1 cup onion in food processor. Process until fairly smooth. Mix with onion in bowl. Spoon in shallow 6-cup baking dish.
Bake in 375 degrees oven 20 minutes. Stir. Bake 10 minutes. Cool slightly. Serve with crackers or toast. Makes 16 servings.