Begin by preparing the cauliflower. Remove the leaves and stem from the head of cauliflower, then cut it into florets. Using a food processor or box grater, rice the cauliflower until it resembles small granules.

Place the riced cauliflower in a microwave-safe bowl, cover it, and microwave on high for about 5-7 minutes. This step helps soften the cauliflower. Allow it to cool slightly before handling.

Once cooled, transfer the riced cauliflower to a clean kitchen towel or cheesecloth. Gather the edges and twist to squeeze out as much moisture as possible. This step is crucial to achieving crispy hash browns.

In a mixing bowl, combine the drained cauliflower, beaten egg, shredded cheddar cheese, chopped green onions, garlic powder, onion powder, salt, pepper, and coconut flour. Mix thoroughly until all ingredients are well combined.

Heat the olive oil or avocado oil in a large skillet over medium heat. Form the cauliflower mixture into small patties, about 2-3 inches in diameter, and carefully place them in the hot skillet.

Cook the hash browns for about 4-5 minutes on one side, or until they are golden brown and crispy. Flip the patties gently and cook for another 4-5 minutes on the other side.

Once cooked, remove the hash browns from the skillet and place them on a paper towel-lined plate to absorb excess oil. Serve immediately for the best texture.