Heat 2 tablespoons vegetable oil in a large skillet over medium heat until shimmering.
Add the finely minced onion and a pinch of the divided salt; cook, stirring occasionally, until the onion is translucent, about 3–4 minutes.
Add the minced garlic and cook until fragrant, about 30 seconds to 1 minute.
Add the ground chuck, season with a little of the remaining salt, and cook, breaking it up with a spoon, until lightly browned and no longer pink, then drain excess grease if needed.
Stir in the sliced hot dogs and cook until heated through and slightly browned, about 2–3 minutes.
Add the banana ketchup, tomato puree, and tomato sauce to the meat mixture; stir to combine and reduce heat to low.
Add 4 ounces (about 1/2 cup) water, stir, and simmer the sauce gently for about 10 minutes, stirring occasionally.
While the sauce simmers, cook the spaghetti in a large pot of salted boiling water according to package directions; drain and keep warm.
Taste the sauce after simmering and add the 2 teaspoons sugar if it tastes too acidic; adjust seasoning with the remaining salt and freshly ground pepper to taste.
To serve, portion the cooked spaghetti onto plates, top with generous sauce, and sprinkle shredded easy-melt cheese over each serving.
