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© Meredith Corporation. All rights reserved. Used with permission.
For caramelized onion: In a large nonstick skillet, melt butter over medium-low heat. Add onion. Cook, covered, for 15 minutes, stirring occasionally. Uncover; stir in thyme, sugar, salt and 1/2 teaspoon pepper. Cook, stirring occasionally, over medium-high heat for 14 to 16 minutes more or until onions are extremely tender and golden. Remove from heat; set aside.
Cut meat crosswise into four slices. Place each slice between two pieces of plastic wrap. Use the flat-side of a meat mallet or a rolling pin to lightly pound meat to 1/2-inch thickness. Discard plastic wrap. Season beef with the remaining 1/8 teaspoon pepper.
For charcoal grill: Place meat on rack of uncovered grill directly over medium coals. Grill steak for 3 minutes, turning once halfway through. (For a gas grill: Preheat grill. Reduce heat to medium. Place meat on grill rack over heat. Cover; grill as directed.) Remove meat from grill. Top each steak evenly with the reserved caramelized onions and blue cheese. Return meat to grill. Grill 2 to 3 minutes more or until cheese begins to melt.
Meanwhile, heat 2 teaspoons butter on a griddle over medium heat. Lay two buns, cut sides down on griddle pan. Toast buns for 2 to 3 minutes or until golden brown. Repeat with remaining butter and buns. Serve steaks on toasted buns.