Place potatoes in large stockpot and add enough cold water to cover. Cover and bring to boil over high heat. Reduce to low and simmer 3 minutes. Add broccoli; don’t stir. Cover and cook 4-5 minutes, or until tender. Drain.
Mix egg, breadcrumbs, salt, pepper and garlic powder in large bowl until just combined.
Add potatoes and broccoli to food processor. Pulse 8-10 times until finely grated. Add to breadcrumb mixture and stir to combine.
Use tablespoon to scoop potato mixture into 40 mounds. Shape each into an oval and place on parchment-lined baking sheet.
Bake 10 minutes; flip and bake 10 minutes, or until golden brown.
Notes
You don't HAVE to peel the potatoes, if you prefer the skin on, go ahead!