Clean the girolles mushrooms (preferably do not wash them).
In a casserole, melt 1 third of the butter with the oil and brown the chops on both sides ; then add salt and pepper, turn the flame down, cover, and let cook for 6 minutes.
Meanwhile, peel and mince the shallot ; melt 1 third of the butter and gently fry the shallot in it. When well soft, spread with the paprika, mix with a wooden spoon and add the sour cream. Simmer for 5 minutes.
In another pan, fry the girolles into the left butter. Turn the flame down then let the girolles cook for 5 minutes ; add salt and pepper. Then top with the cream sauce and mix very carefully.
Display the chops on a (heated) plate then top with the girolle and cream sauce.
Serve right away with fresh pasta (tagliatelle type).