Preheat the oven to 210 degrees. Scrub the sweet potato clean and cut it into wedges with the skin on. Toss them with two tablespoons of olive oil, the smoked paprika, salt, and pepper, and roast for thirty-five minutes, turning halfway through, until they have dark caramelized edges.
For the chimichurri, finely chop the parsley, oregano, garlic, shallot, and red chili pepper as finely as possible. Stir everything in a small bowl with the red wine vinegar and a pinch of salt, then pour three tablespoons of olive oil over it. Let the sauce sit for at least fifteen minutes so the raw garlic can mellow in the acid.
Remove the bavette from the refrigerator well before cooking and pat it bone dry. Season with salt and pepper. Heat a grill pan or skillet until smoking hot and sear the meat for two to three minutes per side for rare to medium-rare. Then, let it rest under foil for five minutes.
Slice the bavette into thin strips, paying close attention to the grain: bavette has a coarse, clearly visible grain, and you must slice against the grain to get tender slices. Slicing with the grain will make the same piece of meat tough.
Cut the little gem lettuce into quarters and arrange everything on a plate. Generously spoon the chimichurri over the meat, along with any resting juices.