Peel the potato, then use a food processor fitted with the shredding blade to shred the potato. Alternatively, use a handheld grater to shred the potato. Then, shred in the zucchini and onion.
Place shredded potato/onion/zucchini mixture into a cheesecloth or thin kitchen towel and wring out any excess liquid into the sink.
Place the dry, shredded mixture into a bowl and add the egg, potato starch, salt, and pepper. Mix until well combined.
Heat oil in a medium-large skillet with high sides, on the stove over medium-high heat. To test if oil is ready, drop in a tiny piece of the potato mixture – if it starts to sizzle, it’s ready.
Lower the heat to medium to prevent oil from splattering. Scoop ¼ cup of the latke mixture and press down into the measuring cup to squeeze out any excess liquid. Then, place into the pan. Only fry 3-4 latkes at a time to prevent overcrowding. Cook latkes for 2-3 minutes on one side, then flip and cook another 2-3 minutes.
Drain latkes onto a paper towel lined plate or baking sheet.
To keep latkes warm and crisp, place onto a pan in a 200°F oven for up to 15 minutes before serving.
To make the sauce, place the parsley into a blender or food processor. Process until finely chopped. Then, add in the remaining ingredients and pulse until combined. Serve sauce with latkes.