Sauté the aromatics: In a medium to large skillet over medium heat, melt the butter. Add the onion and celery, and season with ½ teaspoon kosher salt. Cook, stirring occasionally, until softened and translucent, 4 to 5 minutes.
Add the mushrooms: Add the sliced mushrooms to the pan. Stir to coat them in butter, and season with ½ teaspoon kosher salt and black pepper. Cook, stirring occasionally, until the mushrooms are softened (they won’t necessarily brown, and that’s fine) and cooked down to about half their volume, about 5 minutes.
Deglaze with sherry: Add the sherry or white wine and stir frequently until the liquid has nearly evaporated, about 2 minutes. (If omitting the alcohol, skip this step.)
Make a roux: Sprinkle the flour over the skillet and stir until no dry pockets remain and the raw flour has slightly cooked, about 1 minute. Add the chicken broth and heavy cream and stir well. Bring the mixture to a simmer, then lower the heat to medium-low and let thicken and reduce slightly, about 5 minutes. Add chicken and vegetables: Add the cooked chicken, diced pimentos, and frozen peas (no need to defrost). Stir well and cook until chicken is heated through and peas are hot, 2 to 3 minutes. Season to taste with salt and pepper and serve with rice, if desired.Chicken à la king can be stored in an airtight container for up to 4 days. To reheat, add to a pan on the stove with a splash of water and cook over medium heat for 3 to 4 minutes.