Cut the tomatoes in half crosswise and scoop out all of the seeds. Place the tomatoes, cut side down on paper towels and let drain, 1 hour. In a small saucepan, combine the chopped basil and 1/4 cup olive oil. Heat over low heat just until the oil sizzles. Remove from the heat and let sit until cool, 1 hour. Strain and discard the basil.
Heat a charcoal grill. Brush the cut side of the tomatoes with 2 tablespoons basil oil. Place on the grill, 3" from the heat source and grill until the flesh blackens, 4 to 5 minutes. Turn the tomatoes and char on the other side, 1 minute. Remove . Cut the tomatoes into 1" chunks and place in a bowl. Add the basil oil, red onion, vinegar, and thinly sliced basil. Season to taste with salt and pepper.
Oil the steaks and grill on one side until golden brown, 4 to 5 minutes. Turn the steaks, season with salt and pepper and continue to cook until medium rare, 4 to 5 minutes. Remove from the grill and place on individual plates. To serve, top with the charred tomato salad and serve immediately.