- Preheat the grill, setting the burners to medium. Oil the grate.
- In a bowl, toss the vegetables with the oil. Season with salt and pepper. Place on the grill. Cook for about 10 minutes or until tender. Let cool. Remove the skin from the pepper. Cut the pepper and mushrooms into strips and set aside.
- Spread the pesto and mayonnaise on the cut side of the bread. Layer with the cheese slices, ham and grilled vegetables. Close the sandwich.
- Place the sandwich on the grill and cook for 5 to 10 minutes. With a large spatula, carefully flip the sandwich halfway through cooking so the bread is toasted on both sides. If needed, shut off the burners, close the lid and finish cooking with any residual heat to allow the cheese to melt. Let rest for 2 minutes before cutting.
Square foccacia is available in some grocery stores and bakeries. If unavailable, substitute with ciabatta buns.