Cut a ½-inch slice off the top of each tomato. With a small knife cut around the inside of the fleshy part of the tomato (do not cut through the bottom of the tomato) to within ½ inch of the skin. With a teaspoon, scoop out the tomato flesh, leaving about ½ inch of flesh attached to the skin. Discard the juice and seeds to make room for the stuffing. Turn the tomatoes, cut side down, on a plate lined with paper towels to drain.
Mince two of the garlic cloves, and then mix with 1 teaspoon salt, ½ teaspoon pepper, and the chile powder. Lightly brush the steaks on both sides with oil and season with the spices. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
In a food processor chop the remaining garlic clove, and then add the basil and a pinch of salt; process until the basil is finely chopped. With the processor running, add ¼ cup plus 2 tablespoons oil in a slow, steady stream, stopping to scrape the inside of the bowl once or twice. Pulse in the cheese. Add the bread crumbs and pulse until thoroughly combined. Add the pine nuts and pulse a few times to combine and chop the nuts coarsely; season with salt. Lightly season the tomato cavities with salt and pepper, and then spoon in the bread crumb mixture, packing it down to fit in as much as possible and mounding additional crumbs on top (you will not need all of it).
Grill the steaks over direct medium heat, with the lid closed, until cooked to your desired doneness, 8 to 10 minutes for medium rare (depending on the thickness of the steak), turning once or twice. At the same time, grill the tomatoes over direct medium heat until softened and the topping is slightly browned, 6 to 8 minutes. Remove from the grill and let the steaks rest for 3 to 5 minutes.
Cut the steaks into thin slices, and then garnish with the remaining bread crumbs. Serve warm with the tomatoes.
Note: If you can’t find hanger steak, substitute with skirt steak or flat iron steak.