Step 1

Pound 2 pounds boneless chicken breasts one at a time: Place 1 chicken breast in a gallon-sized zip-top bag and pound with a rolling pin or the flat side of a meat mallet to an even 1/2-inch thickness.

Step 2

Pat the chicken dry with paper towels and season all over with 1 teaspoon of the kosher salt and 1/4 teaspoon black pepper.

Step 3

Heat 2 tablespoons olive oil in a 10-inch or larger skillet over medium-high heat until shimmering. Working in batches, add the chicken and sear until deeply browned, 5 to 7 minutes per side. Transfer the chicken to a plate.

Step 4

Reduce the heat to medium and add 2 tablespoons unsalted butter. When melted, add 8 ounces sliced cremini mushrooms and the remaining 1/2 teaspoon kosher salt, and cook, stirring occasionally until tender, about 5 minutes. Add 2 tablespoons all-purpose flour, stir to evenly coat the mushrooms, and cook for 1 minute.

Step 5

Stir in 1 cup half-and-half or whole milk, 1/2 cup chicken broth, and 2 tablespoons balsamic vinegar until no lumps from the flour remain. Bring to a boil. Reduce the heat to a simmer. Return the chicken and any accumulated juices to the pan and simmer until the sauce is thickened and the chicken is cooked through, 2 to 3 minutes.