To a shallow plate, add the flour, garlic, and salt & pepper. Use a fork to evenly mix.
Dredge the pieces of pork in the flour mixture, liberally coating all sides. Use your fingers to press the mixture in, if needed. Shake off any excess, and transfer to a clean surface until needed.
Add the butter & oil to a large skillet, and melt over medium high heat. Once melted, let the skillet get hot and smoky, then add the battered pork to the skillet.
Let the pork chops cook until golden brown. Flip the chops, cooking until the other side is also golden brown.
Lower the heat to medium low, add the mushrooms, shallots, and garlic. Stirring to evenly combine.
Add the wine and broth, stirring to combine and scrape up the bits on the bottom of the pan, until combined.
Stir in the fresh thyme leaves, cover, and let the mixture simmer for 5-8 minutes.
Stir in the mustard, and let the mixture simmer for another 2-3 minutes, uncovered. When the sauce has thickened to a gravy-like consistency, it's done.
Remove the skillet from heat. Serve the pork chops over a bed of rice, with sauce and mushrooms spooned over top.