If pork chops are thicker than ¼-inch, place between cling wrap and pound to ~¼-inch thickness.
Mix flour, salt and pepper in a pie plate; place each pork chop in the flour mixture and turn to coat on all sides; shake off the excess. Mix a heaping tablespoon of the flour remaining into broth.
Heat half the oil in a large skillet over medium-high heat; place half the chops in skillet and cook until lightly browned, ~4 minutes per side; transfer to a plate; cover loosely with foil; repeat with the remaining oil and pork.
Add butter to skillet; when butter is melted and bubbling, add the mushrooms; cook, stirring frequently, ~5 minutes.
Increase heat to high, add wine; cook and stir until alcohol has evaporated (aroma is gone); add broth, mix, reduce heat to low and simmer uncovered ~3 minutes, stirring continuously until sauce is thickened.
Return the pork to the skillet and simmer ~2 minutes.
Remove from heat; stir in the sour cream.
