Preheat the oven to 350 degrees F (175 degrees C). Grease a mini muffin tin with oil.
Bring water and quinoa to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until quinoa is tender, 15 to 20 minutes. Drain any excess liquid and let cool briefly.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add cauliflower, cover, and steam until tender, 2 to 6 minutes.
Mix cooked quinoa, steamed cauliflower, carrots, Cheddar cheese, eggs, kale, flour, flax seeds, chia seeds, garlic, onion powder, salt, and pepper together in a bowl. Spoon mixture into the muffin cups and press down lightly.
Bake in the preheated oven until edges are light brown, 10 to 12 minutes. Let cool in pan, about 5 minutes. Remove bites from pan and let cool, about 5 minutes more.