Add broth, soy sauce, and sesame oil to the bottom of a slow cooker and stir. Add beef strips and toss to coat.

Turn the slow cooker to low and cook for 5-6 hours. About an hour before it's done, take some of the sauce and add it to a small bowl. Let it sit to cool down for a few minutes. Once cooled, whisk in the cornstarch. Slowly stir the slurry into the slow cooker. Add the broccoli and stir to coat. Continue cooking for the remaining time until broccoli is heated through. Serve.