Preheat the oven to 350 ℉, then brown the ground beef in a large, oven-safe skillet or Dutch oven set over medium-high heat. As it cooks, use a spatula to break it into smaller pieces. Once the beef is cooked, carefully drain excess fat from the pan.
Add the olive oil, butter, and onion to the cooked ground beef. Cook, stirring often, until the onion begins to soften and turn translucent.
Stir in the minced garlic, dijon mustard, pepper, and salt, and cook until fragrant, about 30 seconds.
Sprinkle the beef and onions with the all-purpose flour, mixing well to combine. Cook for about 1 minute, stirring continuously, before adding the beef broth and diced tomatoes. Increase the heat to high and bring to a simmer.
Stir in the pasta and cook for approximately 3-4 minutes less than the time indicated on the package for al dente pasta (this will help prevent the pasta from becoming soggy). Stir often.
Add the heavy cream (at room temperature) and ketchup. Once combined, remove from heat and slowly stir in 1 cup of the shredded cheese until melted, then sprinkle the remaining 1 cup of cheese over the top.
Transfer to the oven and bake for 15-20 minutes or until the cheese is melted and bubbly around the edges.
Serve garnished with sliced green onions, pickles, and lettuce, if desired.