Heat olive oil in a large Dutch oven or deep skillet over medium-high heat. Season generously with salt and pepper. Brown the beef in batches until nicely browned on all sides. Remove and set aside.
In the same pot, add the carrots, onion and celery. Cook for 4–5 minutes until softened. Add the garlic and cook for 30 seconds until fragrant.
Sprinkle flour over the vegetables and stir for about 1 minute. Slowly pour in the beef broth, stirring constantly to avoid lumps.
Stir in Worcestershire sauce, tomato paste, salt, pepper, paprika, thyme, and rosemary. Add the browned beef back in.
Bring to a gentle boil, then reduce heat to low. Cover and simmer for 45-50 minutes, stirring occasionally, until the beef is tender. If the beef isn't tender enough yet, continue cooking another 10-15 minutes. Add extra beef broth or water, as needed, if the stew is getting too thick.
Gently stir in the frozen mini pierogi and 1 cup frozen peas. Simmer uncovered for 5–7 minutes, just until the pierogi are soft and heated through.
Stir in butter for extra richness. Taste and adjust seasoning. Garnish with fresh parsley and serve warm.