In a small bowl, combine consomme, soy sauce, brown sugar, oil, and garlic. Pour over beef. Cook on low for 6-8 hours.
In a cup, stir cornstarch and sauce form the crock pot until smooth. Add to crock pot. Stir well to combine. (If your sauce is not thickening, try bringing your sauce to a boil on the stovetop with the corn starch mixture. Boil until your desired consistency is reached).
Add broccoli to the crock pot. Stir to combine.
Cover and cook an additional 30 minutes on high (the sauce has to boil for it to thicken).