Heat the olive oil in a large, deep skillet over medium-high heat.
Add the ground beef and cook it until it starts to brown, breaking it up into small pieces with a spatula.
Add the diced onion and minced garlic, and continue cooking until the onion becomes soft and translucent.
Season the mixture with Worcestershire sauce, mustard, salt, black pepper, and smoked paprika. Stir well to combine.
Pour in the beef broth and canned diced tomatoes (including their juice). Stir everything together and bring the mixture to a simmer.
Add the uncooked pasta, stir to combine, then reduce the heat slightly and cover the skillet. Let it simmer for 8–10 minutes, stirring occasionally, until the pasta is tender.
Add the diced bell pepper and fresh spinach. Cook for a few more minutes until the vegetables are tender and the spinach is wilted.
Sprinkle the shredded cheddar and American cheese into the skillet. Stir until the cheese is fully melted and the dish becomes creamy and cheesy.
Garnish with chopped pickles if desired, and serve hot.