Step 1: Preheat the oven broiler.
Step 2: Slice the pork on an angle into 1-inch-thick pieces; season with 1/2 teaspoon salt.
Step 3: Heat a large ovenproof skillet over medium-high heat; add 1 tablespoon olive oil. Add the onion, peppers and mushrooms and season with remaining salt; cook until the vegetables are crisp-tender and slightly browned, about 6 minutes. Transfer to a plate.
Step 4: Add the remaining 2 tablespoons oil to the skillet. Add the pork and sear over high heat until browned, 2 to 4 minutes per side. Transfer the pork to the plate with the onion and peppers.
Step 5: Reduce the heat to medium and add the garlic, sage and tomato paste to the skillet. Cook, stirring, until the tomato paste turns brick-red, about 1 minute.
Step 6: Pour in the wine and bring to a boil. Add the broth and return to a simmer. Arrange the pork in a single layer in the skillet; add onion and peppers and sprinkle with the cheese.
Step 7: Transfer to the oven and broil until the pork is cooked through, 4 to 7 minutes. Serve.
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