Place potatoes in a pot of cold water and bring to boil. Reduce heat to simmer for about 20 minutes until potatoes are soft. Meanwhile, prepare vegetables. Preheat oven 400 degrees F and lightly spray baking sheet lined with parchment paper.
Heat oil in a large skillet on medium heat. Add onion, garlic, and ginger, saute until onions are softened about 3 minutes. Add cumin, turmeric, cilantro, carrot, peas, green beans, corn, and salt. Cook until vegetables are tender.
When potatoes are tender, drain them using a colander and rinse with cold water. Mash potatoes with a potato masher or a fork, add cooked vegetables and stir to fully combine. Shape mix into balls, then flatten.
Combine gluten-free flour in a bowl with coconut flour and a pinch of salt.
Dip patties in flour mix, place on a greased baking sheet. Brush or spray with oil. Bake for 40 minutes, turning halfway.