First I started with 4 pork chops, which I sprinkled on both sides with salt and fresh pepper and let sit for about 10 minutes.
I melted a half-stick of butter and about 4 tablespoons of olive oil in a large skillet over high heat, then when it was sizzling, I carefully arranged the pork chops so they fit. I then fried the chops on one side for 1 minute, then the other side for another minute. Then I covered the skillet, reduced the heat to low, and cooked the chops for 5 minutes, flipped them over again, and cooked covered for another 5 minutes.
Then I removed the chops to a plate and sprinkled about 3 tablespoons of flour into the skillet and turned up the heat. I stirred the flour and pan juices with a wire whisk until the raw flour taste was cooked out and the flour was well incorporated. Then I slowly added a 1/2 cup of red wine and 1-1/2 cups of beef stock, whisking the whole time so that the gravy was smooth. Then I cooked it on medium heat for a while until the sauce had thickened and most of the alcohol was cooked out.
Spoon rice onto a plate, arrange the chops on top, then drizzle with the gravy.