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Heat oven to 200C/180C fan/gas 6. Put the chicken on a large baking tray, drizzle with 1 tsp oil and season well. Cook for 20 mins.
Toss the veg in the remaining 2 tsp oil and some seasoning, scatter around the chicken and return to the oven for 30 mins.
Meanwhile, prepare the sauce. Heat the remaining 1 tsp oil in a pan, add the shallot and poppy seeds, and cook for 5 mins. Add the paprika, chicken stock, honey, lemon zest and juice, and simmer until the liquid has reduced by half. Add the soured cream and some seasoning, bubble for 2 mins, then add half the parsley and keep warm until the chicken is ready. Remove the chicken and veg from the oven, scatter with the remaining parsley and serve with the sauce.