Make buttermilk biscuits, don't cook them yet, refrigerate until the filling is ready.
Cook the chicken. To poach, put chicken in medium size sauce pan. Add enough water to cover. Add large pinch of salt. Maybe throw in a bay leaf. Bring to a boil, reduce heat to a simmer, cover the saucepan and simmer gently until chicken is done throughout. Cooking time depends on the number and size of chicken, could be 10 to 15 minutes, though check doneness earlier with smaller pieces. Discard poaching liquid and set cooked chicken aside.
Preheat oven to 400° F. Precook fresh green beans in microwave till just tender.
Heat oil in Dutch oven on stove top over medium heat. Add onion, carrots, green beans, corn, and peas. Add a sprinkling of salt. Sauté until onions soften, about 5 - 7 minutes or so.
Cut chicken into bite-size pieces. Combine chicken with sautéed vegetables, stir well, transfer to a large bowl and set aside.
Melt butter over medium heat in Dutch oven. Add the flour and cook, stirring constantly for 1 minute, until bubbly.
Add chicken broth, milk, thyme, salt and pepper, then whisk assertively. Bring to a boil, whisking continuously. Reduce heat to a simmer, cook 1 minute more, whisking continuously as sauce thickens. If desired, season to taste with more salt and pepper.
Stir in sherry. If sauce is too thick, stir in 2 Tablespoons milk, return to simmer. Add chicken-vegetable mixture to white sauce. Stir thoroughly.
Pour filling into 13 x 9 inch pan. Place uncooked biscuits directly on top of filling, spacing them out evenly. (Put any extra biscuits on separate baking sheet.) Bake until biscuits are done and filling is bubbly, about 20-25 minutes. Start checking for doneness after 18 minutes. Cool slightly and serve.