Combine milk, chives, garlic, salt, and paprika in a medium saucepan, and bring to a boil over high heat. While whisking, slowly sprinkle in polenta. Reduce heat to medium-low; cook, stirring occasionally with a wooden spoon, until polenta has thickened, 5 to 8 minutes. Add Parmesan and butter; stir until combined. Pour polenta into an 8 1/2-inch springform pan; let rest until completely set, about 45 minutes at room temperature.
Preheat the broiler. Remove the outer ring from the springform pan. Cut the polenta into eight wedges. Coat with olive-oil spray, and place on a rack in the oven several inches underneath the broiler. Broil the polenta until golden brown on top and heated through, about 8 minutes. Serve.