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For steaks, in a shallow dish, combine flour, paprika, 1/2 teaspoon salt and 1/4 teaspoon pepper. Dredge steaks in flour mixture (reserve any remaining flour mixture). In a very large skillet, heat 1 tablespoon oil over medium-high heat. Reduce heat to medium. Cook steaks in hot oil for 8 to 10 minutes or until medium doneness (160°F), turning once halfway through cooking time. Top with cheese for the last 2 minutes of cooking time. Remove steaks from skillet; keep warm.
While steaks are cooking, place tomatoes in a food processor. Cover and process with several on-off pulses until tomatoes are coarsely chopped.
For tomato gravy, in the same skillet, heat the remaining 2 tablespoons oil over medium heat. Add garlic; cook and stir for about 1 minute or until golden brown. Stir in the tomatoes, sage, the remaining 1/4 teaspoon salt and 1/2 teaspoon pepper and any remaining flour mixture. Bring to a boil; reduce heat. Simmer, uncovered, about 5 minutes or until desired consistency. If desired, place a small handful of arugula on each of four dinner plates. Place steaks on plates. Spoon some of the tomato gravy over steaks; pass the remaining gravy.