Heat 1 tbsp butter + 1 tbsp olive oil in a Dutch oven; brown 4 chicken thighs on both sides.

Add 2 cups chicken broth; simmer until cooked through. Transfer chicken to a plate and broth to a glass bowl.

Melt 3 tbsp butter in the Dutch oven; add diced onion, carrots, celery, sauté until soft. Stir in garlic and thyme until fragrant.

Sprinkle flour over vegetables; stir to coat. Whisk in reserved broth + milk; simmer until thickened. Stir in sherry.

Cut chicken into cubes, then chicken, green beans, and parsley; remove thyme sprigs.

Place The Unsalted Chef pie crust over filling (see Pie Crust Recipe)

Bake at 375°F until crust is golden and filling is bubbly, about 25–30 minutes.