Prepare the aromatics:

In a large skillet set over medium heat, melt the butter. Once melted, add the diced onion and celery, and sprinkle with half of the kosher salt. Cook, stirring occasionally, until the vegetables soften and become translucent, approximately 4 to 5 minutes.

Cook the mushrooms:

Introduce the sliced mushrooms to the skillet, stirring to ensure they are well-coated in the butter. Season with the remaining salt and black pepper. Continue cooking, stirring intermittently, until the mushrooms have softened and reduced in size by about half, around 5 minutes.

Deglaze the pan:

Pour in the sherry or dry white wine, stirring constantly, and allow the liquid to reduce by half, which should take about 2 minutes. If you prefer to omit the alcohol, simply skip this step.

Create the roux:

Sprinkle the flour evenly over the ingredients in the skillet, stirring until there are no lumps and the flour has cooked slightly, about 1 minute. Gradually pour in the chicken broth and heavy cream, stirring thoroughly to combine. Bring the mixture to a simmer, then reduce the heat to medium-low. Let it cook, stirring occasionally, for approximately 5 minutes, allowing the sauce to thicken and reduce slightly.

Finish the dish:

Add the cooked chicken, diced pimentos, and frozen peas to the skillet, stirring to combine. Continue to cook for 2 to 3 minutes, ensuring the chicken is heated through and the peas are hot. Taste and adjust seasoning with salt and pepper, as desired. Serve the Chicken à la King over cooked rice, if preferred.

This comforting dish can be stored in an airtight container in the refrigerator for up to 4 days. To reheat, simply return it to a skillet, adding a splash of water to loosen the sauce, and warm it over medium heat for about 3 to 4 minutes.