Preheat oven to 425˚. Cut broccoli into roughly equal-sized florets, keeping as much of the stem as possible. Toss with sliced onion, 1 tablespoon olive oil, salt, and pepper. Roast until broccoli is just starting to char, 15-18 minutes.
Bring a pot of water to a boil with a pinch of a salt. Add pasta and cook until tender but not mushy. Drain, reserving at least 1 cup of water.
Place cooked broccoli in blender or food processor with remaining olive oil, lemon juice, almonds, and cheese. Puree, add 2-3 tablespoons pasta water at a time, until a thick sauce forms (will look more like a dip than a sauce). Taste and add more salt/pepper as desired. Combine with hot pasta.
Serve with a sprinkle of slice almonds and extra cheese.