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Preheat your oven to 425.
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Place peeled quartered potatoes in a large pot and cover with cold water. Bring water to a boil and cook potatoes until fork tender.
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Remove the potatoes from the water to cool enough to handle. You will want them to still be warm.
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Grate the zucchini and squash on the large side of a grater.
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In a clean dish towel, squeeze out the excess liquid of the zucchini and squash.
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Grate the potatoes and add them into the bowl with the grated zucchini and squash.
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Sprinkle with the 1½ teaspoons of salt.
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Use a potato masher to help mix everything together.
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Line a large cookie sheet with parchment paper.
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Use your hands to form mixture into small tater tot shapes, about 1 tablespoon of mixture per tater tot.
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Place the cookie sheet in the freezer for about 10 minutes to allow them to firm up.
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Brush the top of each tater tot with a small amount of olive oil and sprinkle each one with salt.
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Bake tater tots until browned on a few sides and crispy, about 40 minutes flipping them halfway though.
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Serve with ketchup.