Cut the cauliflower florets into pieces. Discard the hard stem, and place the remaining pieces in the bowl of a food processor. (You may need to do this in 2 batches depending on the size of your food processor.) Pulse the raw cauliflower until it’s broken up into little bits that are the size of rice. Set aside.
In a large mixing bowl, mix together the eggs, shallots, flour, baking powder, and salt. Add the cauliflower and stir to combine.
Heat 2 tablespoons of the avocado oil in a large skillet over medium heat. Scoop the batter into the pan in 1/4 cup portions, and flatten each one with a spatula to make a pancake shape. (I do 6 at a time in my large cast iron skillet. You can get multiple pans going at once if you don’t have a very large skillet.) Cook over medium for 4 minutes, then carefully flip each pancake. They’re a bit delicate, so they may not flip properly if you try to flip them before 4 minutes. Cook for 4 more minutes on the second side. (Turn the heat down just a little bit if they’re getting too dark.) Continue this process with the remaining batter, adding the final 2 tablespoons of oil when the pan seems dry.