Preheat oven to 350 degrees. Melt butter in oil in large cast iron or other oven proof skillet over medium high heat.
Trim pork chops and pound to 1" thickness. Salt and pepper each side of pork chop and sprinkle lightly with thyme.
Dredge each chop in flour, dusting off excess. Immediately place in pan and sear on first side about 5 minutes. Turn chops and put skillet in oven on bottom rack. Bake until cooked through, 12 to 15 minutes. Use instant read thermometer to check they have reached 165 degrees.
Allow chops to stand for 5 minutes before serving with Cherry Salsa.