Place potatoes in a large pot and cover with cold water. Bring water to a boil and cook potatoes for 20-30 minutes, until fork tender but still have some give in the middle. Drain water and let potatoes cool until they are comfortable to handle. You want them to still be warm.
2
Preheat oven to 425 degrees Fahrenheit. Grate potatoes on the large side of a box grater and put into a large bowl. Grate each zucchini and squeeze out the liquid using a clean dishtowel. Place grated zucchini into the bowl with the potatoes and add 1½ teaspoons salt. Use your hands to mix everything together.
3
Line a large cookie sheet with parchment paper. Use your hands to form small cylinders with the mixture. Use about 1 tablespoon per tater tot. Place the cookie sheet in the freezer for about 10 minutes to allow them to firm up.
4
Brush the top of each tater tot with a small amount of olive oil and sprinkle each one with salt. Bake tater tots until browned a crispy, about 30 minutes flipping halfway though. Serve with ketchup if desired.