In a large Dutch oven or heavy pot over medium heat, heat oil. Add beef and cook, turning occasionally, until seared on all sides, about 10 minutes. Transfer beef to a plate.

Coat bottom of pot with oil if needed and heat over medium-high heat. Cook onion, carrots, and celery, stirring occasionally, until softened, about 7 minutes; season with salt and pepper. Add garlic and tomato paste and cook, stirring, until garlic is fragrant and tomato paste is darkened, about 2 minutes.

Return beef and any accumulated juices to pot. Add broth, wine, Worcestershire, thyme, and bay leaves. Bring to a boil, then reduce heat to medium-low and bring to a simmer; season with salt and pepper. Cover and simmer, stirring occasionally, until beef is tender, 30 to 45 minutes.

Add potatoes and simmer, covered, until potatoes are tender, about 15 minutes.

Remove bay leaves and thyme. Stir in peas and cook, stirring, until warmed through, about 2 minutes; season with salt and pepper.

Divide stew among bowls. Top with parsley.