Preheat the oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.
Bring a pot of water to a boil. Add broccoli; boil until tender, about 5 minutes.
Place 1/2 the broccoli into a food processor or blender. Pulse until broken down into smaller, finer pieces. Transfer to a clean cheesecloth over a large bowl. Repeat with remaining broccoli. Twist the cheesecloth to squeeze out the liquid. Transfer broccoli to a mixing bowl.
Chop cauliflower into small pieces in the food processor. Transfer to a clean cheesecloth over the large bowl. Twist and squeeze out excess moisture. Transfer cauliflower to the mixing bowl.
Mix shredded Mexican cheese blend with the vegetables in the mixing bowl. Stir in coconut flour, onion powder, garlic powder, salt, and pepper. Add eggs; mix well. Scoop out about 1 tablespoon of the mixture onto a flat work surface and roll into a 'tot' about 1 inch tall and 3/4 inch wide. Repeat shaping the remaining mixture and place tots on the prepared baking sheet.
Bake in the preheated oven, turning the pan as needed, until tots are evenly golden brown, 25 to 30 minutes.
