Start by bringing a large pot of salted water to a boil. Cook your lasagna noodles until they're almost done but still firm, about 2 minutes less than what the package says. This will prevent them from getting mushy later. Drain and rinse with cold water, then lay them flat on a surface brushed with oil to keep them from sticking together.
Heat oil in a large pot over medium heat. Cook the sliced hotdogs until they're lightly browned, about 2 minutes, then set them aside. In the same pot, cook your onions and garlic until they're soft and smell good, then add the bell peppers and cook until tender.
Add your ground beef to the same pot and cook until it's no longer pink, breaking it up as you go. Pour in the tomato sauce, banana ketchup, beef broth, and tomato paste. Add the Italian seasoning and sugar. Let it come to a boil, then lower the heat and let it simmer with the lid on for 45 minutes, stirring now and then. Put the hotdogs back in during the last 10 minutes of cooking. Taste and add salt and pepper as needed.
While your meat sauce is simmering, make the white sauce. Melt the butter in a large pan over medium heat. Add the flour and whisk it continuously for 2 minutes – it should smell slightly toasted but not turn brown. Slowly pour in your milk while whisking constantly to prevent lumps. Keep cooking and stirring until the sauce thickens enough to coat the back of a spoon, about 5-7 minutes. Season with salt and pepper.
Heat your oven to 375°F. Grease a 13x9-inch baking pan. Start layering by spreading a thin layer of meat sauce on the bottom, followed by some white sauce. Place a layer of noodles to cover the surface, cutting pieces to fill any gaps. Spread one-third of the remaining meat sauce over the noodles, then add white sauce. Do these layers two more times. On the final layer, top everything with shredded cheese.
Cover the pan with foil, but make sure it's not touching the cheese (you can stick a few toothpicks in the lasagna to hold the foil up). Bake for 30-40 minutes until everything is hot and bubbly. Here's the important part: let it rest uncovered for 15-20 minutes before cutting. This will help your pieces stay neat and hold their shape when you serve them.
Want to make sure it's perfect? Look for these signs: the cheese should be completely melted and slightly golden, the edges should be bubbling, and when you stick a knife in the middle, it should feel hot throughout. If you're making it ahead, you can assemble everything, cover it, and refrigerate for up to a day before baking. Just add an extra 10-15 minutes to the baking time if it's coming straight from the fridge.