Use a paper towel to pat the pork chops dry and season each side with salt and pepper. Dredge the pork chops in flour, shake off the excess and set aside.
In a large skillet, heat the oil and only 3 tablespoons (45 g) of butter until hot and shimmery.
Carefully add the pork chops to the skillet, if they don’t all fit, work in batches. Allow the pork chops to sit, undisturbed, for about 7 minutes to properly sear them. Flip them over, and sear the other side for 4-5 minutes. Note that they will be still be under-cooked. Remove the pork chops from the skillet and set aside under a tented piece of aluminum foil. Repeat with any remaining pork chops, if necessary.
If the skillet has accumulated too much fat, drain off the excess, making sure to leave about 3 tablespoons worth of fat in the skillet for flavor.
Add the remaining butter, onions and red pepper flakes. Saute until the onions are just about tender and translucent (they’ll finish cooking with the pork).
Remove the skillet from the heat and add the wine. Return to a medium heat and stir. Deglaze the pan by scraping up any browned bits at the bottom of the pan, stirring them into the wine mixture. Add the olives. Bring the mixture to a full boil.
Return the pork chops to the skillet (by this time, all the pork should fit in the skillet). Add a light layer of pesto on top of each pork chop. Lower the heat and simmer for another 10-15 minutes (the pork is done when it reaches 145 F.).
Garnish with chopped fresh herbs.
Notes
How do you know when the pork is done? When pressing your finger into the flesh, you should encounter a slight resistance, though it shouldn’t be solid. This takes practice. Give it a try! (and double-check with a meat thermometer until you can use this method confidently. The pork should be 145 F).Serve this dish family style. Bring the entire skillet to the table and let your family or guests serve themselves from there. This skillet will be hot though, so take proper care if there are children present and don’t forget to protect your table. I usually use a thick place mat with a trivet on top if serving this way.