Cut halloumi cheese in slices and set aside. Thinly slice peppers and eggplant. Brush 6 eggplant slices with olive oil and grill 2 minutes per side. Sautée peppers and grill halloumi cheese about 2 minutes per side. Warm the hamburger buns on the grill and finally, top each half with baba ganoush, grilled vegetables, halloumi and some spinach.