Combine the balsamic vinegar, 3 tablespoons olive oil and minced garlic in a small bowl. Whisk to combine then brush over both sides of the cleaned portobello mushrooms. Set aside for 30 minutes while preparing the onions.
Heat the remaining 1 tablespoon olive oil over medium-high heat. Add the onions and cook, stirring frequently, until the onions being to brown, about 5 minutes. Reduce the heat to medium-low and add the 2 tablespoons water. Cook and stir occasionally for about 15 minutes or until the onions are slightly browned and very soft. Add the wine, 1/4 teaspoon salt and pepper, and cook for another 5 minutes or until the wine is evaporated. Cover, remove from the heat and set aside.
Preheat the grill to medium.
Sprinkle the mushrooms with the remaining 1/4 teaspoon salt and pepper. Grill with the gill side down for about 5 minutes. Turn the mushrooms over and cook until they start to release their liquid, about 5 minutes. Turn the mushrooms back over to grill the gill side for another 2 or 3 minutes.
Remove from the grill and place about 1/8 of the blue cheese on each mushroom on the gill side.
To serve top each with 1/4 of the onions and place cheese/onion side up on a bun.
Spread the remaining blue cheese on each bun, add the tomato and lettuce and serve.
Recipe adapted from May/June 2012 Eating Well Magazine