Preheat the oven to 375 degrees F. Combine the mustard, vinegar, chopped rosemary and 1/2 teaspoon each salt and pepper in a bowl; brush all over the pork. Heat 1 tablespoon olive oil in a large nonstick ovenproof skillet over medium-high heat. Add the pork and cook until browned on all sides, about 5 minutes. Transfer the skillet to the oven and roast until a thermometer registers 145 degrees F, about 15 minutes. Transfer the pork to a cutting board and let rest.
Wipe out the skillet. Add the remaining 1 tablespoon olive oil, the garlic and red pepper flakes; cook over medium heat, 2 minutes. Add the broccoli, 1/4 cup water and 1/4 teaspoon salt. Cover; cook 5 minutes.
Bring 3 cups water, the milk, rosemary sprig and 1/4 teaspoon salt to a boil in a saucepan over medium heat; discard the rosemary. Whisk in the polenta and cook, whisking, until thickened, 3 to 5 minutes. Remove from the heat and stir in the parmesan. Slice the pork and serve with the broccoli and polenta.