Pat beef dry. Season with salt and pepper, then toss with flour to lightly coat.
Heat olive oil and butter in a heavy pot over medium-high heat.
Brown beef in batches until deeply seared on all sides. Transfer to a plate.
Add mushrooms to the pot. Cook until browned and their liquid evaporates. Set aside with beef.
Sauté onion, carrots, and celery in the pot until starting to soften, about 5 minutes.
Stir in garlic and tomato paste. Cook 1 minute, stirring, until fragrant and darkened.
Pour in red wine. Scrape up browned bits and simmer 2 minutes to reduce slightly.
Return beef and mushrooms to the pot. Add broth, Worcestershire, thyme, rosemary, and paprika.
Stir in potatoes. Bring to a simmer, then cover and reduce heat to low.
Cook gently until beef is fork-tender, 90 to 120 minutes, stirring occasionally.
Mix cornstarch with water. Stir slurry into stew and simmer 3 to 5 minutes to thicken.
Fold in peas and heat 2 minutes. Adjust salt and pepper, then finish with parsley.