Preheat the oven to 400°F. Line two rimmed baking sheets with high-heat-resistant parchment paper and spray them with olive oil.
Place the cauliflower florets in a large microwave-safe bowl. Add ¼ cup of water. Cover and microwave on high until tender, stirring midway through cooking. Frozen florets will need a total cooking time of about 7 minutes, and fresh florets will need a total cooking time of about 5 minutes.
Drain the cauliflower florets well and place them on a clean kitchen towel to dry. Add them to your food processor and process until coarsely chopped.
Add the eggs, kosher salt, black pepper, garlic powder, and cayenne pepper to the food processor bowl. Briefly process to combine.
Add the almond flour and cheddar and process until combined.
Using a 2-tablespoon scoop, transfer mounds of the mixture to the prepared baking sheets. Each baking sheet should hold 12 mounds, evenly spaced. Gently flatten them, just a little, with the back of a spoon.
Spray the tots with olive oil spray. Bake them until the bottoms are golden brown, about 15 minutes. Flip them to the other side, spray with more oil, and bake until set, about 10 more minutes.
Serve immediately.
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Notes
Using the food processor is easy, but it means the bites are smooth. They don't have the little textured pieces typical of traditional tater tots. If you prefer a coarser texture, chop the cauliflower very finely and mix the ingredients by hand. This will give you better control of the bites' texture than using the food processor.
You can pan-fry these bites in a nonstick skillet over medium heat, about 3 minutes per side, or until golden brown. Make sure not to crowd them in the pan, and cook in batches if necessary. But it's easier to bake them.
You can keep the leftovers in an airtight container in the fridge for 3-4 days. Reheat them in the microwave at 50% power. They are also good when served cold! You can also freeze these bites in a single layer in freezer bags for up to three months.