London Broil and Portobello Sandwich

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1 1/2 pound London broil

1/2 cup olive oil, plus more for brushing steak

Salt and pepper

1/4 cup balsamic vinegar

4 portobello mushroom caps, cut in slices

1 Vidalia onion, cut in rings

1/2 cup mayonnaise

1 tablespoon grated horseradish or grainy mustard

1/2 cup chopped fresh parsley

1/2 lemon, juiced

4 pieces ciabatta bread, split horizontally

1/4 pound Fontina, sliced

1/3 cup (packed) coarsely chopped arugula leaves