Heat grill or grill pan over medium heat.
In a food processor or blender, combine 1/4 of garlic (about 1/2 teaspoon), 1 tablespoon thyme, beans and 1 teaspoon oil: process to form a smooth and spreadable paste. If mixture it too thick, add 1 teaspoon water. Season with pepper and pulse to combine. Set aside.
Combine remaining garlic, tablespoon thyme, and oil on a plate or baking pan. Gently toss musroom caps in the mixture. Season with pepper and drizzle with vinegar. Lightly coat onion slices with cooking spray; grill until lightly charred on both sides. Transfer onions to a clean plate; keep warm.
Grill mushrooms stem side up until browned and juices have begun to collect in centers, about 5 minutes. Flip mushrooms, and continue cooking until center is tender, about 4 minutes more.
Split hamburger buns in half and place cut side down on grill; cook until warm and toasted. Spread 1/4 cup puree on bottom half of each bun, top with two grilled musroom caps. Layer each with sliced cheese, grilled onions, and a small handful of arugula. Top each with matching roll halves, and serve.
To clean mushroom caps, wipe with a damp paper towel; do not rinse or soak them because they will remain soggy even after cooking.
0 servings
* The % Daily Value (DV) tells you how much a nutrient in a serving of food contributes to a daily diet. 2,000 calories a day is used for general nutrition advice.