Place mushrooms stem side down on an ungreased 15 x 10-inch baking pan. Bake for 8 minutes. Transfer mushrooms stem side down to paper towels to cool. Wipe out the pan.
Meanwhile, drain or pat (with paper towel) pesto to remove any excess oil. Combine asiago and pesto in a bowl.
Return mushrooms stem side up to the pan. Fill with asiago mixture. Bake for 10-12 minutes or until mushrooms are tender and cheese is melted.