Soak the cashews in one cup of water and set aside.
Preheat oven to 190F and line two baking trays with parchment paper.
Use a peeler to slice the zucchinis into thin slices.
Mix the oil with 3 teaspoons of the vinegar and a 1⁄4 teaspoon of salt in a bowl. Add the zucchini slices. Mix well and set aside for 5 minutes.
Lay the zucchini strips onto the prepared trays and bake for 2-3 hours in the oven, flipping over after an hour. Cook until crisp and golden.
Once the cashews have soaked for approximately 3 hours, drain and place in a blender with 1⁄4 cup of water, the lemon juice, remaining 1 teaspoon of apple cider vinegar and mustard. Blend until smooth to form the vegan sour cream.
Divide zucchini chips evenly into two portions and serve with vegan sour cream for dipping.
Leftover chips can be stored in an airtight container in the cupboard for 1-2 days. Leftover sour cream can be stored in an airtight container in the fridge for 2-3 days.