Preheat oven to 425 degrees.
Heat 1 Tbsp. of oil in a medium pan. Add the onions and cook on medium heat, stirring constantly for 5 minutes until caramelized. Remove from heat and set aside.
Place the mushroom caps, smooth side up, in a shallow dish. In a small bowl, whisk together vinegar, oil, oregano, garlic, salt, and pepper. Pour over the mushrooms. Let stand at room temperature for 15 minutes or so, turning twice. Place caps on a baking sheet and roast at 425 degrees for 20 minutes, until tender.
In a small bowl mash the avocado with 1 Tbsp. olive oil, lemon juice, cumin, and salt and pepper to taste. Toast the buns for a few minutes. Assemble the burgers with mushroom caps, caramelized onions, avocado, a chard leaf and your favorite burger accompaniments. Serve with lots of napkins!