Preheat the oven to 180C/160C Fan/Gas 4.
Place a large, deep ovenproof frying pan on the hob. Add half the butter and half the oil, and turn the heat low to cook until the butter melts.
Season the chicken breasts with salt and pepper and fry them in the butter and oil. You may need to do this in batches.
Cook the breasts for two minutes on each side until golden brown. Remove them from the pan and set aside.
Add the remaining butter and oil to the pan, tip in the shallots and fry over high heat for five to 10 minutes or until lightly golden brown.
Put the flour in a bowl, whisk in eight tablespoons of the stock, and mix until smooth. Add the mixture to the pan and boil, then pour in the remaining stock.
Seasoning is worth adding now, so throw in the lemon thyme before returning the chicken to the pan.
Cover the pan with a lid and cook in the oven for about 20 minutes or until the chicken is cooked.
Trim the tip from each asparagus spear before serving and slice the stems into short, even lengths. Cook the tips and sliced stems in boiling salted water for two to three minutes, then drain.
Stir the lemon juice, crème fraîche and parsley into the pan with the chicken to complete the sauce. Add the sliced asparagus stems and bring to a boil.
Remove the chicken, slice each breast into three chunks and arrange them neatly on a plate. Spoon over the sauce and arrange two asparagus tips in a cross over the top.
Plate up the remaining ingredients and serve the chicken piping hot.
