Cook the Quinoa and Potatoes: Boil the quinoa according to the instructions on the packaging. At the same time, boil the diced potatoes until tender, then drain and set aside to cool.
Sauté the Vegetables: Heat 1 tablespoon of vegetable oil in a large pan over medium heat. Add the minced onion and cook for 2-3 minutes until softened. Add the chopped mushrooms, red pepper, and mashed garlic. Cook for another 5-7 minutes, stirring occasionally, until the vegetables are soft and the moisture from the mushrooms has evaporated.
Prepare the Veggie Ball Mixture: In a large bowl, mash the boiled potatoes. Add the cooked quinoa, sautéed vegetables, parsley, paprika, cayenne pepper, sesame seeds, salt, and pepper. Mix everything thoroughly until well combined.
Shape the Veggie Balls: Using your hands, form the mixture into small balls, about the size of a golf ball. If the mixture feels too dry, add a small amount of water or oil to help bind it.
Cook the Veggie Balls: Heat the remaining tablespoon of vegetable oil in a large skillet over medium heat. Cook the veggie balls in batches, turning them gently every few minutes, until they are golden brown and crispy on all sides, about 8-10 minutes total. Alternatively, you can bake them in the oven at 375°F (190°C) for 20-25 minutes, flipping halfway through.
Serve: Once cooked, serve the veggie balls warm with your favorite dipping sauce or as a part of a main dish with salad or grains.