Preheat the slow cooker.
Melt 1 tablespoon of the butter in a large frying pan with the oil and add the chicken pieces. Cook over a medium–high heat for a few minutes, turning occasionally, until browned all over.
Tip the potatoes into the slow cooker and spread them out over the base, then transfer the chicken from the frying pan and place on top. Add the lemon juice and zest, garlic and capers.
Dissolve the chicken stock pot in 200ml boiling water, then pour into the slow cooker followed by the wine. Add the remaining butter and a good pinch of salt and pepper. Cook for 6–7 hours on LOW or 3–4 hours on HIGH.
At the end of the cooking time, ladle out a little of the juice from the slow cooker and put it in a saucepan over a low heat. Mix the cornflour with a little cold water, then add this to the saucepan. Cook for a few minutes until it starts to thicken, then stir it into the juice in the slow cooker. Pop the lid back on and cook for another 20 minutes or so until it thickens. You can prepare some veggies to serve with it in the meantime.
Taste and check the seasoning, then stir in the parsley. Serve the piccata with green veggies or a salad.