Preheat the oven to 400°F. Line two baking trays with parchment paper*.
In a small bowl, whisk together the ground flaxseed meal with ½ cup warm water to make a flax “egg”. Set aside while you prepare the rest of the recipe.
Using a hand grater or food processor, grate the potatoes and carrots. Transfer to a clean kitchen towel or nut milk bag (my favorite method!) and squeeze out the excess liquid over the sink. Transfer the potatoes and carrots to a large bowl, then add the onions, salt, and pepper. Stir in the flax “egg”, then sprinkle with the flour and mix well. The mixture should be fairly moist, but if it’s overly wet and won’t hold together, add 1 to 2 tablespoons flour and mix again.
Rub or brush approximately 1 tablespoon olive oil onto the parchment-lined baking trays, making a thin layer of oil. Spoon heaping tablespoons of batter onto the baking sheets, flattening with a spatula or your fingers to make a thin pancake. Repeat until all the batter is used, then brush the top of each pancake with a little more oil. Transfer the trays to the preheated oven.
Bake the latkes for 15 minutes, then flip them over and bake for 10 to 12 minutes more, until the latkes are golden brown and crisp around the edges. Remove from the oven and serve immediately.
*Note – For extra-crispy latkes, skip the parchment paper and bake directly on the oiled metal baking tray. This method yields a crispier result but does require that you have a thin metal spatula that can get under the latkes without breaking them. The parchment method works just fine and also reduces clean-up time. Either way works!