Combine 1 Tbl of ground flax with 3 Tbl of water. Allow to sit for at least 10 minutes to thicken.
In the bowl of a food processor, add the chickpeas, green onion, parsley, salt, pepper and garlic. Pulse a few times until it's a coarse mixture. Remove to a large bowl.
No need to clean the processor, just add the carrots and mushrooms. It is imperative that the mushrooms (if using canned) are squeezed completely dry. Process until finely minced. Add to the chickpea mixture.
Add the flax mixture, flour and panko breadcrumbs. Stir to combine. If it seems to moist, add more flour or panko. It will still be sticky, but should be workable. Damp hands make forming the cutlets easier.
Using a handful of the mixture, form into a ball and then into a rough cutlet shape. Proceed directly into the breadcrumbs. Completely coat the formed cutlets in light coating of flour. I found it simpler to do this when patting between my hands.
Heat a pan over medium high to high heat and add oil suitable for pan-frying. Add the cutlets to the pan 1 at a time and fry until golden on one side. Flip and repeat. Remove to paper toweling to cool.
Combine all of the ingredients for the dipping sauce and serve warm.