Make onion rings: Pour oil into a 4-qt. saucepan to a depth of 2"; heat over medium-high heat until a deep-fry thermometer reads 350°. Meanwhile, put onions and milk into a bowl; let soak for 20 minutes. In a large bowl, whisk together remaining paprika and salt, flour, chili powder, cayenne, cumin, salt and pepper. Working in batches, remove onions from the milk, shake off excess, and toss in seasoned flour. Fry onions until crisp, about 3 minutes. Drain on paper towels; season with salt. Set aside.