Heat oil in large nonstick skillet over medium heat. Add onion and saute for 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 two bread slices. Place bread, buttered side down, on a platter. Layer onion, ham, cheese, and endive on top of the bread slices. Top each with another bread slice, buttered slice face up.
Heat another large nonstick skillet over medium heat. Add sandwiches and cook until bread is golden brown and cheese melts, pressing occasionally with a spatula, about 4 minutes per side. Cut sandwiches in half diagonally and serve immediately.
