Add a teaspoon of sesame oil to a skillet and place over medium-high heat. Add the onions, and saute for 3-5 minutes to soften.
Then place the beef, onions, garlic, and ginger in a large slow cooker. Whisk the brown sugar, sherry, beef base, soy sauce, remaining sesame oil, and cornstarch together. Pour over the beef and stir to combine. Then cover and turn on high for 2-3 hours, or low for 6-8 hours.
When the beef is soft, stir in the broccoli and cover again for 20-30 minutes. Once the broccoli is tender (but not mushy) serve warm with steamed rice or cauliflower rice.
This broccoli beef recipe could easily be turned into a Paleo Recipe by making the substitutions above.