In a skillet melt the butter and add the chicken to it.
Add the chopped onions to the skillet and cook the chicken and onion for a couple minutes so the chicken is no longer pink and the onion becomes translucent.
Add the chopped carrots and celery to the skillet.
Sprinkle the flour over the chicken and vegetables and stir. Slowly add the white wine and chicken stock and season with salt and pepper. Add the peas as well at this point, and stir.
Bring to a boil and simmer for about 15 minutes so that the carrots and celery are tender. While the chicken mixture is cooking, cut the biscuits. Remove the chicken mixture from heat and divide evenly among the ramekins. I used 4 ramekins for this, 2 bigger ones 4 inches in diameter and 2 smaller ones, about 2 inches.
Place the biscuits on top of each ramekin and cut a couple slits in each.
Brush the biscuits with egg and place on a baking tray and bake in a preheated oven at 375 F degrees for about 15 to 20 minutes, until the biscuits are nice and golden brown.