Top each of 2 bread slices with ham, Manchego, and remaining slices. Brush tops of panini with 2 teaspoons oil.
In a large nonstick skillet, heat remaining oil over medium-low. Place panini in skillet, oiled side up. Cover; cook until golden brown and cheese has melted, 5 to 8 minutes per side, pressing down with a spatula 3 to 4 times during cooking.
Meanwhile, make dipping sauce: In a small bowl, mix together jam and Dijon. Serve panini with sauce on the side.