Place chicken breast between two sheets of wax paper or plastic wrap. Pound each breast with the flat side of a meat mallet until approximately 1/2 inch thick.Cut each in half to make them more manageable.
Combine flour with fine sea salt, ground black pepper and garlic powder. Dredge all chicken in flour mixture and set aside.
Heat butter and olive oil in large skillet over medium high heat. Working in batches, brown chicken on each side until fully cooked, approximately 3-4 minutes per minutes.
Set aside, leaving all the browned bits in the pan. There should still be a little residual butter or oil in the pan. If not, add an additional tablespoon of butter.
Add mushrooms, garlic and shallot, sauteing until mushrooms shrink in size and shallots soften.
Add dried thyme, dry white wine and heavy cream over medium heat.
When hot, add shredded asiago cheese, stirring until it thickens and fully combines.
Add chicken back to the mixture, coating and reheating for 2 minutes.
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