Prepare a barbecue so the coals are medium-hot, then preheat the grill.
Combine the garlic, vinegar, salt and pepper, then whisk in the olive oil. Cut off the stems of the portobellos and use a moist cloth to remove any dirt from the caps. Place the mushrooms in a bowl, then pour the vinaigrette over them. Toss to combine.
Place the mushrooms gill-side up directly on the grill. Grill until they are tender and juicy, about 8 to 10 minutes.
When the mushrooms are almost done, place the hamburger buns on the grill and toast for a few minutes.
Season the mushrooms with a sprinkle of salt and pepper and place in the buns. Top with crumbled Gorgonzola and some greens. Serve with condiments.