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Cook the potatoes in a small pan of boiling water for 10-15 mins until tender. Drain, then leave to steam-dry and cool.
Heat the oven to 180C/160C fan/gas 4. Line a six-hole muffin tin with paper or silicone cases. Tip the eggs, chorizo, peas, parsley and some seasoning into a large bowl. Slice the cooled potatoes into rounds that are the thickness of a £1 coin, and add these to the bowl. Mix gently.
Spoon the mixture into the cases, ensuring each has some of the potato, chorizo and peas. Sprinkle the cheese on top and bake for 15-20 mins until golden and set in the middle. Check the frittatas are set by shaking the tin gently – there should be no wobble. Leave to cool slightly and eat warm, or cool completely and chill for up to 24 hrs.