Shred the zucchini coarsely and toss it with a little salt. Let it stand for 5–10 minutes so the salt can draw out excess moisture.

Transfer the zucchini to a clean kitchen towel or several layers of paper towel. Squeeze it very thoroughly, working in two batches if needed, until little moisture remains.

Heat the oven to 400°F (200°C). Line a baking sheet with parchment and lightly grease it, or lightly grease a mini-muffin pan; a preheated metal pan can help the bottoms brown.

Combine the drained zucchini, egg, breadcrumbs, cheddar, grated onion, garlic powder, black pepper, and remaining salt in a mixing bowl. Add any optional Parmesan, herbs, Italian seasoning, or smoked paprika, then mix until the ingredients hold together when pressed.

If the mixture seems wet, mix in 1–2 additional tablespoons of breadcrumbs. Scoop roughly 1 tablespoon at a time and shape each portion into a small cylinder or nugget.

Arrange the tots on the prepared baking sheet with space between them, or place them into the greased mini-muffin pan. Bake for 8–11 minutes, turn each tot, and continue baking for another 8–11 minutes until browned and firm.

For a more deeply crisped surface, broil the tots for 1–2 minutes at the end, watching closely so they do not burn. Rest them for several minutes before serving.