If you'd like to, steam the tempeh for 10 minutes.
Whisk together the tamari, vinegar, syrup, garlic, ginger, and red pepper flakes. Place the tempeh cubes in a rectangular or square glasslock container and pour the marinade over them. Cover the container and allow the tempeh to marinate for a couple hours, or overnight in the fridge.
Preheat your oven to 400F. Line a baking sheet with parchment or foil and coat it with vegetable oil spray. Remove the tempeh cubes from the marinade (reserving the marinade) and arrange them on half of the baking sheet. Arrange the broccoli on the other half. Pour the marinade over the tempeh and vegetables. Roast for 35 minutes, or until the tempeh and broccoli are browning, flipping the tempeh cubes once halfway through cooking.
Serve the tempeh and broccoli over rice, noodles, a salad, or whatever you like. Sprinkle with sesame seeds if desired.