Prepare barbecue (medium-high heat). Combine first 6 ingredients in processor; add 2/3 cup oil and puree until almost smooth. Season chimichurri with salt and pepper.
Brush pepper strips, steaks, and cut side of bread with remaining 1/4 cup oil. Sprinkle peppers and steaks with salt and pepper. Grill peppers until tender, about 5 minutes per side. Grill steaks to desired doneness, about 4 minutes per side for medium-rare. Grill bread, cut side down, until beginning to brown lightly, about 2 minutes. Thinly slice steaks crosswise; divide among bread bottoms. Spoon chimichurri over steak (about 1/4 cup per sandwich), then top with pepper strips. Cover with bread tops and serve.
Recipe Remix:. Toss any remaining chimichurri sauce with potato wedges and roast in 400°F oven until just tender, about 40 minutes.