Prepare the mojo sauce: Use a Microplane to grate the zest from the orange and lime directly into a blender, then squeeze in the juice from both fruits as well. Add olive oil, garlic, oregano, cumin, salt, and pepper; blend until everything is well combined and smooth.
In a small bowl, set aside 2 tablespoons of the mojo sauce for serving. Pour the remaining sauce into a 1-gallon ziplock bag along with the steak. Push out as much air as possible before sealing the bag. Marinate in the refrigerator for at least 1 hour, turning occasionally; several hours or even overnight is preferred for more flavor.
When you’re ready to cook, allow the steak to return to room temperature while you peel, pit, and chop the mangos into bite-sized pieces. Transfer the mango and any juice that has collected into a medium bowl and set aside.
Sear the steak: Take the steak out of the bag and discard any excess marinade. Place the steak on a plate close to the stove. Discard the bag and any leftover marinade.
At the same time, heat a 12-inch (or larger) cast-iron skillet over high heat. Let it heat up for about 3–4 minutes, then add the canola oil, swirling it around to coat the bottom of the skillet. Carefully lay the steak in the hot pan and allow it to cook undisturbed for 3 minutes. Gently flip the steak and place the butter on top. Continue cooking for another 3–4 minutes, occasionally tilting the skillet to spoon the melted butter mixture over the steak, until it reaches your desired doneness (use a thermometer for accuracy: rare – 125°F; medium-rare – 130°F; medium – 135°F).
Keep the heat on under the skillet while you carefully remove the steak and place it on a cutting board to rest.
In the meantime, add the sliced onions to the hot skillet and sauté them for a couple of minutes until they are browned around the edges. Using a slotted spoon, transfer the onions to the bowl with the mango chunks and mix in the reserved 2 tablespoons of mojo sauce.
Slice the steak against the grain into ½-inch thick pieces. Serve with the mango, onions, and lime wedges on the side.