Light a gas or charcoal grill. In a small bowl, combine the shallot, vinegar, salt and black pepper. Let stand for at least 15 minutes, then slowly whisk in the oil. Set aside.
Cut each heart of romaine and the pepper in half, lengthwise (the root will keep the romaine together). Seed the pepper, then lightly drizzle the cut sides of the romaine and pepper with olive oil.
Cook the pepper halves on a hot grill until soft, then remove to a plate to cool. Grill the romaine hearts, cut-side down, for 2 to 5 minutes, until seared. When cool enough to handle, chop the red pepper into strips. Sprinkle the seared romaine, cut-side up, with red pepper strips and shards of the cheese. Dress with the sherry vinaigrette and serve.