Preheat oven to 400°F and prepare a baking sheet with parchment paper.
Remove the leaves from the cauliflower and cut down the center. Cut into large chunks and place half the cauliflower at a time into the bowl of a food processor fitted with a blade. Pulse until very fine, scraping the sides occasionally if necessary. Place all the finely ground cauliflower into a bowl with the salt. Stir and microwave for 1 minute.
Transfer the cauliflower to a cheesecloth and squeeze to remove up to 1 cup of liquid. When it seems you can't get any more liquid to release, measure 2 1/2 cups dried cauliflower packed into a medium bowl.
Add the almond flour, coconut flour, baking powder, jalapeno, cheddar cheese, and 3 eggs. Mix until evenly combined.
Pack the cauliflower mixture into a 1/2-cup measuring cup and run a butter knife along the exterior. Invert onto the baking tray and make a hole in the center. Use your fingers to shape any parts that don't look compact.
Use a silicone brush to break up the remaining egg. Brush the egg wash over the bagels and sprinkle generously with poppy seeds.
Bake for 32 to 34 minutes until dark golden on top, turning the tray halfway through for even baking. Cool the bagels a bit before eating and store in the fridge with a paper towel (to absorb moisture that releases). Enjoy within 3 days or freeze.
Due to the fragile nature of these bagels, I find it best to reheat the bagel whole in a toaster. If you have a toaster oven, that would work even better.Recipe adapted from Kirbie's Cravings - Everything Bagels.