Heat oil in large nonstick skillet over medium heat. Add onions; sauté 5 minutes. Reduce heat to medium-low; cover and cook until onion is very tender and golden, stirring frequently, about 25 minutes longer. Season with salt and pepper. Cool slightly.
Butter 2 bread slices. Place bread, buttered side down, on platter. Spread on 1 teaspoon of mustard. Divide onion, ham, cheese and arugula between bread slices. Top each with another bread slice; butter top slices.
Heat large nonstick skillet over medium heat. Add sandwiches and cook until bread is golden brown and cheese melts, pressing occasionally with spatula, about 4 minutes per side. Cut sandwiches in half diagonally and serve immediately.