Preheat the oven to 350°F Brush 1 tablespoon mustard all over the chicken. Sprinkle with the peppercorns, rosemary and salt to taste, patting gently so the seasonings stick.
Heat a large skillet over medium-high heat; add 2 tablespoons oil. Add the chicken and cook until golden brown, about 6 minutes, turning once. Transfer to a baking dish (set aside the skillet for the sauce); bake the chicken until cooked through, about 10 minutes.
Meanwhile, add the shallots to the skillet; cook over medium-high heat until just soft. Remove the pan from the heat, add the brandy, then return the pan to the heat and scrape up any browned bits. Add the broth, bring to a boil and cook until slightly thickened, about 2 minutes. Stir in the remaining 2 tablespoons mustard and the parsley.
Heat the remaining 1 tablespoon oil in a deep skillet over medium-high heat. Stir in the garlic; cook about 30 seconds. Add the spinach, season with salt and cook until wilted; add the lemon zest. Serve with the spinach.