Crumble beef bouillon cube into warm water in a bowl and stir to dissolve; add soy sauce, brown sugar, garlic, and sesame oil and stir to dissolve sugar.
Put beef strips into a slow cooker crock. Pour sauce mixture over the beef.
Cook on Low for 6 to 8 hours (or on High for 4 hours).
Spoon 2 tablespoons liquid from the slow cooker into a bowl. Whisk cornstarch into the liquid and stir the cornstarch mixture into the liquid in the slow cooker until consistent in color.
Cook on High until the sauce thickens, about 30 minutes.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil.
Cook broccoli in covered steamer until tender, 2 to 6 minutes; add to sauce in slow cooker and stir to coat.
Ladle broccoli beef over portions of cooked jasmine rice and garnish with sesame seeds.
