Step 1

Make the sauce and preheat the slow cooker. Combine the broth, soy sauce, oyster sauce, brown sugar, sesame oil, and garlic in the crock of a 6-quart or larger slow cooker. Stir to dissolve the sugar and set the slow cooker to the HIGH setting.

Step 2

Add the beef and carrots, cover, and cook on high for 4 to 5 hours. Add the sliced beef and carrots and use tongs to coat with the soy mixture. Cover and cook until the beef is cooked through and tender, 3 1/2 to 5 hours on the HIGH setting. Start checking at 3 1/2 to 4 hours, as flank steak tends to cook faster and may be tender at 4 hours.

Step 3

Add the slurry and broccoli and cook for 30 minutes more. Whisk the water and cornstarch in a small bowl until smooth (this is your "slurry"). Add to the slow cooker and stir to combine. Add the chopped broccoli and stir to coat the broccoli in the sauce. Cover and cook until the sauce is thickened and the broccoli is tender, about 30 minutes more.

Step 4

Serve over rice. Serve the finished beef and broccoli over rice.