Season pork chops on all sides with steak seasoning. Mix flour, basil, and bouillon granules together in a small bowl.

Melt 2 tablespoons butter in a large skillet over medium heat. Add seasoned chops and cook until browned and only slightly pink in the center, 7 to 10 minutes per side. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C). Transfer chops to a plate.

Add remaining butter to the skillet as needed so that about 3 tablespoons pan drippings remain. Stir pepper into pan drippings and cook for 1 minute. Add flour mixture and cook, stirring constantly, until browned, about 2 minutes. Gradually whisk in milk and bring to a simmer over medium heat; cook, stirring constantly, until thick and bubbly, 4 to 6 minutes.

Serve hot sauce over pork chops.