Heat a large, heavy-bottomed skillet over medium-high heat. Add the ground beef and let it brown undisturbed for 2 minutes to develop color, then break it up with a spoon and continue cooking until no pink remains, about 4 more minutes. Drain off any excess fat, leaving a thin coating in the pan.
Push the beef to one side, add the chopped onion to the empty space (use 1 teaspoon oil if the pan is dry) and sauté until translucent, about 3 minutes. Stir in the garlic and cook 30 seconds until fragrant.
Stir in the tomato paste, Worcestershire, smoked paprika and dried oregano; cook 1 minute to deepen the flavors and scrape up any browned bits from the pan.
Pour in the beef broth and add the dry pasta. Stir once to combine, bring to a gentle boil, then reduce heat to a steady simmer. Cover with a lid slightly ajar and cook, stirring occasionally, until the pasta is just tender, about 10–12 minutes (timing depends on pasta brand).
When the pasta is almost done, stir in the milk and frozen peas (if using). Continue to simmer uncovered for 1–2 minutes to warm through.
Remove the skillet from the heat. Off the burner, add the shredded cheddar a handful at a time, stirring until melted. Fold in the Greek yogurt until the sauce is creamy and smooth. Taste and adjust seasoning with more salt or pepper if needed.
Let the dish rest, uncovered, for 3–5 minutes so the sauce thickens slightly. Serve hot, garnished with chopped parsley or extra cheddar if desired.