Heat a nonstick skillet over medium heat. Add 1 tbsp olive oil and the sliced onion with a pinch of salt. Cook, stirring occasionally, for 10 minutes until softened. Reduce heat to medium-low, stir in the butter and honey, and cook 10 to 15 more minutes until deeply golden and jammy. Stir in the balsamic vinegar and cook 1 minute. Transfer onions to a plate.

Spread a generous layer of softened goat cheese onto one side of each bread slice, pressing gently to the edges.

Pile the caramelized onions onto two cheese-spread slices. Top each with a handful of arugula, a drizzle of balsamic glaze, and black pepper. Close with the remaining bread, cheese side down, and press lightly.

Wipe the skillet and heat it over medium. Brush the outsides of the sandwiches with olive oil, place in the skillet, and press with a heavy pan. Cook 3 to 4 minutes per side until deep golden and crisp. Slice and serve immediately.