Preheat oven to 400° F. Cut broccoli into large florets. Toss in a bowl with 2 tablespoons olive oil, 1/4 teaspoon salt, garlic powder and Parmesan cheese. Spread onto a large baking sheet and roast for 20 minutes.
Meanwhile, drain and rinse beans. Toss onion and garlic into food processor and pulse until blended well. Add to a large bowl with the beans, bread crumbs, remaining 1/4 teaspoon salt, and pepper. Stir to combine while mashing the beans. Shape into 6 patties.
Add remaining 4 tablespoons oil to a large skillet. Heat over medium until a small amount of water dances when dropped onto the skillet. Add patties one at a time and cook for 2 minutes per side or until golden. Add more oil as needed.
Serve patties with roasted broccoli and sliced nectarines.