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Step 1
Lightly season the pork with salt and pepper. Place the flour in a pie plate and dredge pork until evenly coated on both sides with flour; do not discard the remaining flour.
Step 2
Heat the oil and 2 tablespoons of the butter in large frying pan or cast-iron skillet over medium-high heat until shimmering. Add the pork and sear until dark golden-brown on the bottom, 4 to 5 minutes. Flip and cook on second side for 1 minute more to cook out the floury taste (the pork chops will not be cooked through). Transfer to a plate.
Step 3
Add the mushrooms to the pan and cook, stirring every few minutes, until beginning to brown, about 8 minutes. Add the garlic and thyme and cook until fragrant, about 30 seconds. Add 1 tablespoon of the remaining flour and stir and cook for 1 minute. Stir in the marsala and chicken broth and bring to a simmer. Simmer until reduced and thickened slightly, about 5 minutes.
Step 4
Return the pork chops to the pan, add any juices from the plate, and simmer until the the pork is cooked through and registers at least 145°F on an instant-read thermometer, about 3 minutes more.
Step 5
Remove from the heat. Stir in the remaining 3 tablespoons butter until melted. Taste and season with salt and pepper as needed. Serve with egg noodles or crusty bread, if desired.