Brush the pork chops with olive oil, and season the pork chops with salt and pepper. Set aside and begin to heat the grill/grill pan.
In a large saute pan, heat the oil over medium heat. Add the onion and saute until translucent, about 4-5 minutes. Add the mushrooms and saute until tender, about 4-5 minutes more.
Add the garlic and saute until fragrant. Stir in the tomatoes and broth. Bring the mixture to a simmer and continue to simmer until the liquid mostly evaporates, about 10-15 minutes. It will still have enough liquid to be saucy, but the broth will have reduced and have bolder flavor. Season with salt, pepper, and thyme.
Meanwhile, grill the pork chops until cooked through, about 7-9 minutes (or more, depending on thickness). Serve with sauce.
I always have three kinds of hot sauce in my purse. I have a soft spot for making people their favorite dessert, especially if it's wrapped in a pastry crust. My newest cookbook, The Book on Pie, came out on November 10th, 2020, and my pie merch collaboration with Food52 is out now too: https://food52.com/shop/merchants/manifest-food52/food52-x-erin-mcdowell