Preheat oven to 400°F. Grease a sheet pan. Peel potatoes and cut into 2 inch pieces. Add to a saucepan and cover with water. Bring to a boil. Boil for 5 minutes.
Add broccoli and boil for another 5 minutes. Drain potatoes and broccoli.
Transfer vegetables to a food processor with the remaining ingredients. Blend until combined.
Shape 1 tablespoon amounts of the mixture into tots and place on the greased sheet pan. Makes about 40 tots. (If mixture is a little sticky, lightly grease your hands to prevent sticking to your hands while shaping.)
Spray shaped tots with oil. Bake for 15 minutes. Flip and bake for another 10 minutes.
