Step 1

Heat oven to 400°F. Season eggplant all over with 1/2 tsp salt and let sit 5 minutes.

Step 2

Heat 1/2 Tbsp oil in a large skillet on medium-high. In two batches, cook eggplant, tossing occasionally, until golden brown on all sides, 4 to 5 minutes. Transfer to a plate, reserving any oil left in the skillet. Add 1/2 Tbsp oil and repeat with remaining eggplant.

Step 3

Add bell pepper and garlic to skillet, reduce heat to medium and cook, covered, stirring occasionally, until tender, 8 to 10 minutes, adding a splash of water to the skillet if they begin to stick.

Step 4

Meanwhile, pat steaks dry. Heat remaining Tbsp oil in a large skillet on medium-high. Season steaks with 1/4 tsp each salt and pepper and cook until golden brown on all sides, 6 to 8 minutes total. Remove from heat and drain off any oil. Add vinegar to skillet, then transfer to oven and cook, flipping steak once, to desired doneness, about 8 minutes for medium-rare. Transfer to a cutting board and let rest at least 5 minutes before slicing.

Step 5

Return eggplant to the skillet with pepper mixture and cook, tossing occasionally, 2 minutes. Coarsely grate tomato directly into skillet and bring to a simmer. Fold in basil and serve with steak.