Slice tenderloin tips down center, careful not to cut all the way through. Pound meat flat with back of knife. Preheat broiler. Drain mushrooms, reserving liquid.
Heat 1 tablespoon olive oil in large frying pan over high heat and add garlic. Cook for 1 minute, to release flavor, then add shallots, chiles and 1/2 sliced onion. Add 4 ounces sherry, port and 3/8 cup liquid from mushrooms. Bring marinade to boil.
Lay meat fillets in shallow dish, season with salt and pepper and strain marinade over them, reserving vegetables. Return vegetables to pan and add beef stock. Cook on high heat and reduce until syrupy, to about 1/4 cup. Strain. Rinse out pan and add 1 tablespoon olive oil and add remaining onion. Remove fillets from marinade and dry lightly with paper towels. Add reduced stock, marinade and mushrooms to onions. Reduce. Stir in 1/4 cup butter and cream. Separately combine 1 teaspoon butter with flour. Add this to sauce to thicken. Add paprika and bring to a boil. Add parsley.
Place fillets in broiling pan, brush with remaining olive oil and broil for 4 minutes on each side. Cut avocado into quarters, peel and place pieces under broiler with tenderloin.
To serve, place pieces of avocado on platter, then top each with a tenderloin tip. Add remaining sherry to broiler pan, then mix in simmering sauce. Spoon sauce over meat and avocado pieces.