Pat the steak dry and heavily season both sides with salt and pepper. Set aside at room temperature. In a small bowl, stir together the red onion, ¼ cup lime juice, and a sprinkle of salt.
In a mortar and pestle, mash together the garlic, jalapeño, lime and orange zest, oregano, and 1 teaspoon salt until fragrant. Alternatively, pulse a few times in a food processor. Transfer to a medium bowl and stir in orange juice, cumin, and remaining ¼ cup lime juice.
In a large cast iron skillet, heat the olive oil over medium-high until just smoking. Cook the steak until deeply browned, 2 to 3 minutes per side. (You can also cook the steak on a grill over high heat.)
Immediately transfer the steak to the bowl with the dressing and let rest for 10 minutes, tossing the meat occasionally so all sides absorb dressing. While the steak rests, cut the avocados into chunks and transfer to a medium bowl. Season with salt and pepper, and spoon in some of the red onion and lime juice.
Thinly slice the steak against the grain. Drizzle over more dressing and top with additional red onion, as desired. Serve with avocado alongside.