To make the burgers:
Preheat oven to 375F. In 3-quart, shallow baking dish, toss mushrooms with walnuts, garlic, 1 tablespoon oil, 3/4 teaspoon salt, and 1/4 teaspoon pepper; spread in an even layer. Bake 20 minutes or until mushrooms are tender. Set aside to cool. Turn oven off.
In a food processor, pulse mushroom mixture, red onion, green onions, and vinegar until mostly smooth, scraping side of bowl if necessary. Transfer mixture to a large bowl and stir in quinoa and cornstarch until well-blended. Cover bowl with plastic wrap and refrigerate 2 hours.
Preheat oven to 375F. Line baking sheet with foil. Form mixture into 5 patties (about 1/2" thick and 3" wide). In a 12" nonstick skillet, heat remaining 1 tablespoon oil on medium.
In 2 batches, cook patties 5 minutes or until well-browned, turning over once. Transfer seared patties to prepared baking sheet. Bake 10 minutes or until hot in the centers.
Make the rosemary mayo:
Meanwhile, combine mayonnaise, rosemary, lemon juice, and a pinch of salt.
Keeps up to 5 days, refrigerated.
Serve burgers on buns with rosemary mayo, garnished with sprouts, lettuce, and tomato.

4 medium portobello mushroom caps (about 1 lb), stalks removed, chopped
1/2 cup walnuts
1 clove garlic
2 tbsp. canola oil
1/4 cup Chopped red onion
3 green onions, chopped
2 tsp. rice wine vinegar
1 cup cooked quinoa
1/2 cup cornstarch
Whole-grain burger buns
Sprouts
Lettuce
Sliced tomatoes
Rosemary Mayo
1/2 cup mayonnaise
1 tsp. finely chopped fresh rosemary
1 tsp. lemon juice
Kosher salt