Preheat your oven to 375°F. While it heats, prepare all your ingredients: cut the chicken breasts into 1-inch pieces, cube the potatoes into 3/4-inch pieces, peel and halve the shallots, trim and snap the green beans in half, finely chop the fresh rosemary, and zest the lemon. Having everything prepped and ready before you start cooking will make the process smooth and keep you from scrambling mid-recipe.
Season the chicken pieces with 1 1/4 tsp salt and 1/2 tsp black pepper. Heat 2 tablespoons of olive oil in a large oven-safe skillet over medium-high heat until shimmering. Working in batches if needed to avoid crowding, brown the chicken for about 3 minutes per side until golden on the surface (it doesn't need to be fully cooked through). Transfer the browned chicken to a plate and set aside—this browning step develops deep flavor through the Maillard reaction, which is essential to the final dish.
In a small bowl, whisk together the grain mustard, Dijon mustard, honey, cider vinegar, paprika, garlic powder, cayenne pepper, and 3/4 tsp salt. The cider vinegar is crucial here—it cuts through the richness of the honey and creates a balanced, savory-sweet sauce. Set the sauce aside; you'll drizzle it over everything in the final step.
In the same skillet you used for the chicken (don't wash it—those browned bits add flavor), add the remaining 2 tablespoons of olive oil over medium heat. Add the halved shallots and cubed potatoes, stirring to coat with oil. Sprinkle in the finely chopped rosemary and the lemon zest. Transfer the skillet to the preheated 375°F oven and roast for 15 minutes until the potatoes start to soften and the shallots begin to caramelize.
Remove the skillet from the oven and stir in the trimmed green beans. Nestle the browned chicken pieces from Step 2 back into the skillet among the vegetables, and pour the honey mustard sauce from Step 3 evenly over everything. Return the skillet to the oven and bake for 25-30 minutes until the chicken reaches an internal temperature of 165°F and the vegetables are tender. I like to give it a gentle stir halfway through to ensure the sauce coats everything evenly and the flavors meld beautifully.