Cook the pasta: Bring a large pot of salted water to a boil.
Cook pasta until just shy of al dente (about 1–2 minutes less than package directions). Drain and set aside.
Preheat the oven: Set to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Brown the meat: Heat olive oil in a large skillet over medium heat.
Add ground beef, breaking it into crumbles. Cook until browned and no longer pink, 5–7 minutes. Drain excess fat if needed.
Sauté aromatics: Add diced onion and a pinch of salt to the skillet.
Cook until softened, 3–4 minutes. Stir in garlic and cook 30 seconds more.
Build the sauce: Stir in diced tomatoes, tomato sauce, tomato paste, mustard, Worcestershire (if using), smoked paprika, onion powder, garlic powder, remaining salt, and pepper. Simmer 3–4 minutes to thicken slightly.
Taste and adjust seasoning.
Add the yogurt: Remove the skillet from heat. Let cool 1–2 minutes, then stir in Greek yogurt until smooth. This keeps the yogurt from curdling and adds creaminess.
Combine with pasta: Fold the cooked pasta and diced pickles into the meat mixture.
Stir in 1/2 cup cheddar and the mozzarella (if using) until evenly distributed.
Assemble: Transfer the mixture to the prepared baking dish. Sprinkle the remaining 1/2 cup cheddar evenly over the top.
Bake: Bake uncovered for 15–18 minutes, until the cheese is melted and the edges are bubbling.
Finish and serve: Let rest 5 minutes. Top with extra pickle slices, a light drizzle of ketchup and mustard if you like, and a handful of scallions or shredded lettuce.
Slice into squares and serve warm.