Heat vegetable oil in a large skillet over medium-high heat.
Add beef cubes in batches and brown on all sides, about 4-5 minutes per batch. Transfer browned beef to the slow cooker.
In the same skillet, add chopped onion and cook until softened, about 3-4 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Sprinkle flour over the onions and garlic, stirring constantly for 1-2 minutes to cook the flour.
Gradually pour in the ale, stirring to combine and scrape up any browned bits from the skillet.
Add tomato paste, salt, black pepper, dried thyme, and bay leaves. Stir well.
Transfer the ale mixture to the slow cooker with the beef.
Add sliced carrots, parsnips, and celery to the slow cooker and stir to combine.
Pour beef broth into the slow cooker and stir gently.
Cover and cook on low for 8 hours, or until beef is tender and vegetables are cooked through.
About 15 minutes before serving, stir in thawed peas and chopped fresh parsley.
Remove bay leaves before serving.
Serve the stew hot with crusty bread or mashed potatoes if desired.