Place whole potatoes in a pan with cold water. Bring to a boil. Reduce to a simmer and boil potatoes until they are tender, about 12-15 minutes. Let cool.
Once potatoes are cool enough to handle, peel, then grate potatoes in a bowl on the the largest setting of a box grater.
Grate zucchini. In a cheesecloth or clean towel, squeeze out as much water as possible.
To the bowl of grated potatoes, add finely grated zucchini, nutritional yeast, basil, oregano, and salt and pepper. Mix well.
Using your hands, make tots. Place on a parchment lined baking sheet. Bake at 350°F for 45 minutes, or until crispy, flipping halfway through.