Shred cleaned and peeled beets using a box grater or grater attachment on the food processor, then transfer to a large mixing bowl. Stir in the chopped shallot, flaxseed meal, salt, and pepper, and set aside for 10 minutes. If serving with dill yogurt sauce (optional), add yogurt, fresh dill, salt, and olive oil to a small bowl and whisk to combine. Place in the refrigerator to keep the sauce cool.
To the beet mixture, add the chickpea flour and stir until well combined. Get out a large plate or tray to hold the patties. Form into patties using 1/4 cup (50 g) of the beetroot mixture per patty. Press together in the palm of your hands to form a thin, flat patty. Recipe as written makes ~8 patties.
Heat a large cast iron skillet over medium / medium-high heat for a minute or two and then add 1 Tbsp (15 ml) avocado oil.
Once the oil is hot, swirl to coat the pan. Add only as many fritters as will fit comfortably in the pan. You should hear a sizzling sound that indicates the oil is hot enough. If the oil is splattering, reduce the heat.
Cook for 2-4 minutes, or until underside is browned. Then flip carefully, flatten with the back of a metal spatula, and cook for 2-3 minutes more. Transfer to a plate and repeat with remaining 1 Tbsp (15 ml) avocado oil and fritters.
Serve warm with dill yogurt sauce (optional). Store leftover fritters covered in the refrigerator for up to 3-4 days, or in the freezer up to 1 month. Reheat on the stovetop over medium heat, in a 350 degree F (176 C) oven, or in the microwave until hot. If frozen, thaw slightly before reheating.