Pulse carrots in a food processor until finely chopped, but not pureed.
Heat 1 tablespoon of olive oil in a non-stick skillet. Add carrots and ¼ teaspoon salt. Cook carrots on medium-low until softened (approximately 5-7 minutes), stirring occasionally. Allow to cool 1-2 minutes. While carrot mixture is cooking, rinse out the food processor and set aside.
After the carrots have cooled for 1-2 minutes, add them to the food processor along with chickpeas. Start by pulsing and then, process on low until well combined with some chunks remaining, scraping down the sides as needed.
Transfer chickpea mixture to a large bowl. Add mayo, chickpea flour, nutritional yeast, parsley, garlic powder, onion powder, dill weed, ½ teaspoon salt and white pepper. Use a silicone spatula or spoon to combine.
Separate the mixture into 4 equal pieces and form into balls with your hands. Use your hands to form the balls into *patties, rounding out the the edges.
Heat olive oil over medium in a non-stick skillet. Add chickpea patties to the skillet and cook for approximately 7 minutes per side until golden brown. Be sure to carefully **flip the burgers as they can fall apart easily.
Serve with desired toppings.