Fill a large skillet with enough water to reach a depth of 1 inch and bring to a boil. Add the spinach and cook until wilted, 3 to 4 minutes. Drain in a colander, pressing to remove any excess moisture. Return to the pan and stir in the cream cheese and pepper jack cheese. Cook, stirring, over medium heat until the cheese is melted. Season with salt and pepper and cover to keep warm.
In a large nonstick skillet, melt the butter over medium heat. Add the ham and cook until browned, 2 to 3 minutes on each side. Drizzle with the maple syrup and turn to coat. Serve with the creamed spinach.