Cut each onion in half lengthwise, slicing through root end. Place onions, cut-side down, on a cutting board, then thinly slice into semicircles.
Heat oil in a medium-sized frying pan set over medium heat. Add onions, separating as you add to pan. Sprinkle with salt. Reduce heat so onions are gently cooking but not frying. After about 10 minutes, when onions are just beginning to soften and caramelize, deglaze pan by stirring in wine and scraping up any brown bits from pan bottom. Continue cooking, stirring often, until caramelized, about 30 minutes.
Meanwhile, lightly brush one side of each slice of bread with olive oil. Place half of bread slices oil-side down.Layer each with cheese and ham. Top with the caramelized onions. Sandwich with remaining bread slices placing oil-side up.
Set a large frying pan over medium heat. Add sandwiches. Cook until bread is golden and cheese melts, 3 to 5 minutes per side.
Makes 2 sandwiches.
Delicious wine-glazed caramelized onions, Iberico ham and cheese are the stars of this modern twist on a classic. Perfectly pair this indulgent sandwich with a glass of robust Spanish red wine.