Heat a large skillet over medium-high heat and add the ground beef, breaking it apart with a spoon as it cooks. Cook for 5-7 minutes until the beef is fully browned and no pink remains, then drain any excess fat. I recommend using lean ground beef because it keeps the dish from becoming greasy, which is especially important since we're topping it with cheese and sour cream. Set the cooked beef aside in a bowl.
In the same skillet over medium heat, add the cooked beef back in along with the drained baked beans and corn. Stir in the smoked paprika and chili powder, mixing well to distribute the spices evenly throughout the mixture. Let this simmer for 2-3 minutes, stirring occasionally, so the flavors meld together and the mixture is heated through. The combination of smoked paprika and chili powder adds depth without overpowering the dish.
Arrange the tortilla chips in a single layer on a large baking sheet, then top evenly with the beef and bean mixture from Step 2. Sprinkle the shredded cheddar cheese over the entire layer—I like to make sure every chip gets some cheese so you get melted cheese in every bite. Place the sheet under a preheated broiler for 2 minutes (watch closely as broilers vary), or bake at 350°F for 10-15 minutes, until the cheese is completely melted and bubbly.
Remove the nachos from the oven and let them cool for 1-2 minutes so you can handle them safely. Drizzle or dollop the sour cream over the top and sprinkle the fresh cilantro as a final garnish. Serve immediately while the cheese is still warm and melted.