Whisk Marinade/Glaze ingredients together in a medium bowl. Add 1/4 cup to a large freeze bag along with 1/4 cup olive oil and sirloin cubes. Marinate 2 hours up to overnight (the longer the better) in the refrigerator. Refrigerate remaining Marinade/Glaze separately.
When ready to cook, add broccoli to a large bowl and drizzle lightly with olive oil. Toss to coat. String beef and broccoli on skewers** piercing broccoli at the top of the stem, just below the floret.
Grease and preheat grill to medium high heat. Grill skewers until lightly charred all over, approximately 5 minutes per side. You can cheat and check a a cube for doneness.
Meanwhile, whisk remaining Marinade/Glaze with 1/4 cup water and 1 teaspoon cornstarch, cover and bring to a boil on your grill (this can also be done on the stovetop). Once simmering, uncover and stir until thickened. Brush cooked skewers with Glaze. Serve warm with rice.