Trim excess fat from pork fillet. Season with salt, pepper and garlic. Place fillet in a baking pan and pour orange juice over it. Marinate for at least 2 hours, turning fillet frequently.
Heat butter and oil in a large skillet. Remove pork from marinade and dry with paper towel. Cut fillet in medallions and fry them 3 minutes per side, until golden on both sides.
Combine vinegar with sugar and oregano. Pour over meat and cook over low heat from 3 to 5 minutes. While cooking, stir sauce and turn meat on both sides, to absorb flavor. Correct seasoning.
Garnish with basil sprigs.