Combine cornmeal and broth in a deep saucepan over medium-low heat. Once it starts simmering, cover partially and lower the heat. Cook until thickened but still flowing, about 8-10 minutes.
Heat olive oil in a skillet over medium-high heat. Add garlic and cook briefly, then toss in asparagus and artichoke hearts. Cook for 5 minutes until asparagus is tender-crisp, then add peas with a splash of water and season.
Stir butter, grated Parmesan, chives, parsley, and black pepper into the cooked polenta. Serve by spooning polenta onto plates, topping with vegetables, and finishing with shaved Parmesan.