Steam the veggies: Steam the potatoes, broccoli, cauliflower, and carrots together until fork tender (about 10-12 minutes).
Let cool slightly.
Mash & mix: In a food processor pulse the veggies a few times. It's okay to leave a few small chunks for texture.
Add flavor & binders: Stir in the cheddar cheese, breadcrumbs, egg, garlic powder, salt, and pepper. Mix until well combined. If mixture feels too wet, add a bit more breadcrumbs.
Form tots: Use your hands to shape the mixture into small tot shapes or balls.
Bake: Place tots on a lined baking sheet. Bake at 400°F (200°C) for 18-22 minutes, flipping halfway through, until golden brown.
