Season chicken with salt and pepper. Heat oil in a large skillet over medium-high heat.
Brown chicken 4–5 minutes, stirring so pieces cook evenly; remove to a plate.
Add green beans and a splash of broth; cover and steam 3–4 minutes until bright and tender-crisp.
Stir garlic into beans for 30 seconds, then return chicken to skillet.
Whisk mustard, honey, vinegar, and remaining broth; pour over chicken and beans. Simmer 2–3 minutes until sauce thickens.
Stir in butter if using, adjust salt and pepper, and serve.