Heat vegetable oil in a large skillet over medium-high heat.
Add beef cubes in batches and brown on all sides, about 3-4 minutes per batch. Transfer browned beef to the slow cooker.
In the same skillet, add diced onion and cook for 3 minutes until softened.
Add minced garlic and cook for 30 seconds until fragrant.
Pour in beef broth, soy sauce, oyster sauce, and brown sugar. Stir to combine and bring to a simmer for 2 minutes.
Pour the sauce mixture over the beef in the slow cooker.
Add ground black pepper and salt to the slow cooker and stir gently to combine.
Cover and cook on low for 5 hours.
After 5 hours, whisk cornstarch and cold water together in a small bowl until smooth.
Add broccoli florets to the slow cooker, then pour the cornstarch slurry over the stew.
Cover and cook on high for an additional 1 hour until broccoli is tender and sauce has thickened.
Stir the stew before serving. Adjust seasoning with additional salt or pepper if desired.