Steam the rutabaga cubes until very tender when poked with a paring knife.
In the meantime, put the ground flax seed and water in your food processor bowl. Let it sit for at least 10 minutes to create a "flax egg."
Add the beans, carrot, parsley, flour, paprika, salt, and cooked rutabaga to the food processor.
Pulse for a couple of seconds, then stir with a soft spatula to move the contents around. Repeat this step (pulsing and stirring) two or three more times. The idea is to chop up some of the beans and rutabaga but not all. You don't want a smooth paste by any means! If you don't have a food processor, use a potato masher to create the same effect.
Turn the batter into a bowl and mix briefly with your hands, then form the batter into a mound. Cut the mound into quarters. Form each quarter into a fairly thick patty.
Heat the oil in a skillet, preferably non-stick, over medium-high heat with a bit of the batter. When it begins to gently sizzle add the four patties to the skillet. If you use a cast iron or stainless steel skillet you will need to use more oil so the patties don't stick to the pan.
Cook on the first side until golden brown, flip and cook until golden on the second side.