Heat 3 tablespoons butter in a large, heavy dutch oven. Salt and pepper the chicken parts well.

Cook chicken in the butter until nicely browned on both sides, about 7 minutes per side. Do this in 2 batches if necessary.

Remove chicken to a platter.

Add the chopped onions and leeks and cook about 7 minutes or until softened. Add the sherry and use it to scrape up any brown bits. Simmer till it's mostly cooked off, about 3 minutes.

Add the ¼ cup of milk or cream, 3 cups chicken broth, thyme and bay leaf and bring to a simmer. Add the chicken pieces to the pot and any juices.

Cover pot and simmer for about 30 minutes.

Transfer the chicken to a cutting board to cool slightly. Discard the bay leaf. Allow the sauce to settle for a few minutes, then skim the fat from the surface using a wide spoon.

In a medium bowl, mash butter and flour together with a fork until a paste forms and no flour is still visibly dry. Pour one ladleful of filling over it, and whisk until smooth. Add a second ladleful, whisking again.

Return mixture to the larger pot, stir to combine, and bring mixture back to a simmer for 10 minutes. The sauce will thicken to a gravy-like consistency. If the sauce is too thick, add the additional cup of chicken broth. Adjust seasonings, if needed.

Add carrots and peas to stew and simmer for 3 minutes, until firm-tender. Shred or dice the chicken, discarding the bones and skin or saving it for another use. Return chicken to stew and re-simmer for 1 minute. Stir in parsley.

Heat oven to 375 degrees. Roll out dough large enough to cover either four 2-cup ovenproof bowls or one large (8cup) casserole dish.

Fill bowls leaving about 1 ½ inches below rim for simmering.

Whisk egg with water to make an egg wash. Brush edges of bowls with egg wash so your crust can adhere. Place crust over each bowl or your large casserole. Bake until crust is golden brown and filling is bubbling, about 30-35 minutes.