Preheat the oven to 425 degrees . Place a greased rack on a foil-lined baking sheet. In a large nonstick skillet, heat 2 tablespoons olive oil over medium-low heat. Add the breadcrumbs and toast, stirring, for 6 to 8 minutes. Transfer to a bowl to cool; stir in the parsley and cheese.
Brush the pork with the mustard and coat with the breadcrumb mixture. Arrange on the rack and bake until cooked through but still juicy, 20 to 25 minutes.
Meanwhile, in a clean skillet, heat the remaining 1 tablespoon olive oil over medium-high heat. Add the onion and cook, stirring occasionally, until slightly softened, about 3 minutes. Add the broccoli, season with salt and pepper and toss. Add 1/2 cup water, cover and simmer, stirring occasionally, until crisp-tender, 2 to 3 minutes. Serve with the chops.