All you REALLY need to know about making muffins:
1) The ratio of Flour:Liquid:Egg:Oil is 2:2:1:1 (in weight)
2) Get as much water OUT of your veggies as possible
3) Stir liquids CAREFULLY into the dry ingredients
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Cut your beets, carrot and potatoes in small pieces, put them in a bowl, mix with a tablespoon of salt. Let the salt draw out the water from the vegetables for 5-10 minutes.
Dice your cheddar cheese and onion in very small even sizes.
Squeeze out the juice from the beets, carrot and potatoes, either with your hands or a cheesecloth.
Preheat your oven to 200°C (400°F).
Mix your dry ingredients: Baking powder and flour
Make your flax seeds egg: Mix your flax seeds with water at a ratio 1:2
Mix your wet ingredients in a bowl: eggs, flax seeds, Milk and vegetable oil
Gently blend the above wet ingredients into the above dry ingredients (not the other way around)
Prepare dough for baking: SUPER gently fold the beets, carrot, cheddar cheese, onion and potatoes into the dough.
Distribute a thin layer of butter or vegetable oil in each tin in your muffin tray, to prevent the sponge from sticking to the sides during cooking. Then distribute the dough in the tins.
Bake your 'dough' as muffins for about 30 minutes at 200 C. It is done when you can put a toothpick into the muffins, and it comes out without dough on.