Preheat oven to 350 F. Line a baking sheet with parchment paper.

Peel potatoes and place in a large pot, covered with water.

Bring the water to a boil and then, removing the lid, let potatoes boil in the water for about 5-7 minutes, until fork tender.

Remove potatoes from the water and let cool. Once cooled, grate them using a box grater and place grated potatoes in a large bowl.

Using a paper towel or kitchen towel, squeeze excess water out of the potatoes. Add flour, garlic powder, onion powder, parsley, salt and pepper the bowl. Mix everything together until a thick dough-like texture forms. Set aside.

In a food processor, add chopped broccoli and grind until very small pieces remain.

If not already grated or shredded, grate the cheddar cheese.

Add broccoli and cheese to the bowl with the potatoes and mix until evenly dispersed throughout.

Using your hands, mold heaping tablespoons of the mixture until a rectangular, tot-like shape and place on a plate.

Add olive oil to a large pan over medium high heat. Add the tots (in 2 batches, if necessarily) and heat for about 5-6 minutes, until golden. Then flip and cook for another few minutes on the other side until both of the large sides are browned.

Transfer tots to the parchment-lined baking sheet (optional: place on a paper towel to remove some of the excess oil at this time) and bake in the preheated oven for 10 minutes.