In a small bowl, whisk together the beef broth, soy sauce, brown sugar, ginger, and red pepper flakes, then set it aside.
Slice the beef chuck roast into thin strips and place them in the slow cooker.
Pour the prepared sauce over the beef, add the minced garlic, and stir to combine.
Cook the mixture on low for 6-8 hours or on high for 3-4 hours.
In a separate small bowl, create a slurry by mixing the cornstarch with 1/2 cup of the sauce or water. Stir it well until smooth.
Add the slurry to the slow cooker, stirring it into the beef and sauce. If on low, increase the heat to high and cook for an additional 30 minutes to allow the sauce to thicken.
Stir in the broccoli florets and continue cooking for 20-30 minutes, until the broccoli is tender.
Serve the dish over mashed potatoes, white rice, or pasta for a complete meal.