In a large Dutch oven, add chiles, onion, and garlic. Add just enough water to cover and bring to a boil over high heat. Turn off the heat, cover the pot, and let the ingredients steep for 10 minutes until softened. Add paprika, cumin, chili powder, red pepper flakes, salt, and pepper.
Lightly season beef with salt and pepper. Heat oil in a large skillet over medium-high heat and add beef. Sear for 5 minutes, until browned. Add beef to chile mixture and enough water to cover. Simmer, covered, over medium-low heat for 45 minutes, occasionally using a heatproof potato masher to mix the meat and spices. Remove from heat, set aside to cool, and refrigerate overnight to intensify flavor.
Reheat chili in a large pot over medium heat. Ladle hot chili into bowls and top with cheddar cheese, onion, and pickled jalapeño peppers. Serve with sour cream on the side.