Heat the olive oil over a medium high heat in a large pot and add the chicken. Brown on one side for 5 minutes then flip and brown the other side. Remove the chicken from the pot and place on a plate.
Reduce the heat to medium and add the onion, peppers and garlic. Cook until softened, about 5 minutes, then add the tomatoes and all the spices and return the chicken to the pot. Cover and leave to cook for 20 minutes while you make the polenta.
Bring the milk and chicken stock to the boil in a large pot then add the polenta. Whisk thoroughly and cook for 15 minutes over a medium low heat. Add the butter and cheese and whisk again until everything is combined.
Once the chicken has been cooking for 20 minutes remove the lid and pull out the chicken thighs. Chop up the meat and remove the bones then return the chicken to the sauce and stir together.
Serve the polenta topped with the chicken and whatever other toppings you fancy.