In a skillet, heat a drizzle of oil and a small lump of butter. When the foaming subsides, add the onion and cook for a few minutes, until soft. Add the celery, carrot and mushrooms and cook until they soften, release their liquid and then the mushrooms and onion start to brown a little. Add the herbs at some point while you're cooking them. Sprinkle the flour overtop and cook for a minute, then add the broth and water and bring to a simmer. Let it bubble for at least a minute, then add the chicken and peas and cook for 5 more minutes. If it's too thick, add a bit more stock or water. If it's too watery, keep cooking until it cooks down and thickens. Add the half & half and bring to a simmer again, just to heat it through. Season with salt and pepper and serve over warm biscuits.