Add the olive oil and balsamic vinegar to a small blender and blend well until smooth. Wash and pat dry the portobello caps and transfer them to a sealable container (or zip-lock bag) along with the balsamic marinade. Allow the mushrooms to marinate at least 15 minutes, up to 1 hour.

Heat the grill to medium and brush the eggplant slices with olive oil and sprinkle with salt and pepper.

Place the portobello mushrooms and the eggplant on the hot grill and cover. Cook until grill marks appear, about 2 to 3 minutes for the eggplant and about 5 to 7 minutes for the mushrooms. Flip and continue cooking until vegetables are juicy, tender, and cooked through, about another 2 to 3 minutes for the eggplant and 5 to 7 minutes for the mushrooms. Transfer vegetables to a plate.

Toast two buns with havarti cheese (or your choice) and layer with a grilled portobello mushroom, a few slices of eggplant, roasted red bell pepper, red onion, and arugula. Drizzle on desired amount of pesto sauce and serve.