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Heat the oil in a large flameproof casserole over a high heat and fry the chicken for 5-7 mins until golden all over. Remove to a plate and set aside.
Melt the butter in the same pan, then reduce the heat to medium and fry the onion and carrots for 5 mins until just starting to soften. Sprinkle in the flour and cook for 2 mins more. Slowly add the stock, stirring as you go. Add the mustard and vinegar along with the chicken and cook over a low-medium heat for 30 mins, stirring regularly. Season to taste, then add the peas and cook for 5 mins more. Stir in the cream.
Make the dumplings by mixing the flour with the baking powder, suet or butter, chives (if using) and ½ tsp salt. Swiftly stir in 8-10 tbsp water using a cutlery knife, then bring the dough together using your hands – it should be firm and pliable. Divide into eight equal-sized pieces, weighing for accuracy if you like. Nestle the dumplings on top of the stew, then cover with the lid and cook for 15 mins over a gentle simmer. Remove the lid and slide the pan under a hot grill for 5-10 mins until the dumplings are puffed up and golden brown. Ladle into bowls to serve.