Season the chicken with 1/2 teaspoon salt and the pepper, then toss with the flour until lightly coated.

Heat a large 12-inch skillet over medium-high heat. Add the oil, then add the chicken in a single layer. Cook for 4 to 5 minutes, stirring once or twice, until lightly browned. Transfer the chicken to a plate.

Reduce the heat to medium. Add the butter, onion, and carrots to the same skillet. Cook for 4 minutes, stirring often, until the onion softens and the carrots begin to turn tender.

Stir in the garlic and cook for 30 seconds. Pour in the chicken broth while scraping up the browned bits from the bottom of the skillet.

Whisk in the milk, ranch seasoning, mustard, and remaining 1/2 teaspoon salt. Bring the sauce to a gentle simmer over medium heat.

Return the chicken and any juices to the skillet. Simmer for 6 to 8 minutes, stirring occasionally, until the chicken is cooked through and the sauce lightly thickens.

Stir in the frozen peas and cook for 2 minutes, until warmed through. Serve hot over rice, egg noodles, or mashed potatoes if using.