Season pork chops on all sides with steak seasoning.
Melt 2 tablespoons butter in a large skillet over medium heat. Cook chops in melted butter until browned and slightly pink in the center, about 7 to 10 minutes per side.
Add remaining butter to the pan as needed so that about 3 tablespoons pan drippings remain in the pan when the chops are finished cooking. Transfer pork chops to a plate and return skillet to medium-high heat.
Mix flour, basil, and beef stock cube together in a bowl.
Stir black pepper into skillet with the pan drippings and cook for 1 minute.
Add flour mixture and cook, stirring constantly, until browned, about 2 minutes.
Pour milk into flour mixture;
Cook and stir constantly until mixture is thick and bubbly, 4 to 6 minutes.
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