Dust chicken strips lightly with flour, shaking off excess. Cook in 1 tablespoon olive oil in large skillet until golden brown on both sides but not completely cooked through, about 10 minutes. Remove to dish and set aside.
In same pan, add 1 tablespoon olive oil and cook garlic just until garlic juices are released, about 1 minute. Deglaze pan with white wine, scraping brown bits from bottom.
Add chicken stock to pan and reduce until sauce thickens, about 10 minutes. Add lemon juice, thyme, salt and pepper to taste.
Add chicken back to pan and simmer for about 5 minutes, until no longer pink in the middle and meat has reached internal temperature of 165 degrees F. If sauce becomes too thick, just add a little more wine and a little more stock.
Coat chicken with sauce and add butter. Simmer on low for 2 minutes.
Sprinkle cheese over the top of each breast. Cover and cook just until cheese melts. Serve garnished with parsley.
Serve with fresh angel hair pasta or basmati rice.