Combine the orange juice, garlic, ginger, soy sauce, cornstarch, and red chili paste, if using. Pour half of the sauce, over the steak strips. Reserve the other half of the sauce. Marinate the steak for 10-30 minutes.
While it marinates, cut up the broccoli into florets, if necessary and then the orange.
To slice the orange, slice the top stem and bottom off of the orange. Let the orange rest on one side and carefully cut down and along the orange just against the flesh to remove the white pith and skin. Flip over and cut off any remaining skin & pith. Once all of the flesh is exposed, cut straight down the middle. Lay each piece flat and slice pieces to create fan shapes. Pour any excess juice into the reserved sauce.
Once the steak has had a chance to marinate for a bit, bring a couple of cups of water to a boil in a saucepan with a lid. Add the broccoli florets and steam for 2-4 minutes until the broccoli is to your desired tenderness. Scoop out or strain the broccoli florets and shake off the excess liquid.
Place a large sauté pan or wok over medium-high heat. Shake the marinade off of the steak pieces. Add a splash of the oil into the skillet and quickly arrange the steak in the sauté pan so they are not touching. Sear on one side for 1-2 minutes.
Flip over and sear on the other side for 1-2 minutes. Toss in the broccoli florets. Pour the remaining sauce onto the steak and florets. Toss lightly to combine and cook on the sauce. Toss in the orange slices gently so as not to break them up too much.
Serve on top of the hot brown rice.