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1. Finely grate peel from lime. Cut lime in half and strain juice into a bowl with peel. Using a fork, mash butter with lime peel and juice until thoroughly combined. Wrap butter mixture in plastic wrap and form into a 1-inch-thick log about 5 inches long, twisting ends to close. Chill until firm.
2. Finely chop 2 of the onions and combine with herbes de Provence, thyme, salt and pepper in a small bowl; set aside. Brush remaining onions with 1 teaspoon of oil on both sides of steak, then rub on herb mixture.
3. In a grill pan, heat remaining oil over medium heat. Grill steak 7 to 9 minutes per side, until meat thermometer inserted in the steak reaches 145 degree F for medium doneness. Add onions the last 4 minutes of grilling, turning once. Let steak rest 5 minutes before slicing. Top each serving with 1/4-inch-thick slice of lime butter. Makes 4 servings.