Preheat the oven to 400 degrees F. Mix the chile powder, 1/2 teaspoon salt and 1/4 teaspoon pepper; rub on the steak. Heat a large cast-iron skillet over medium-high heat. Add 1 tablespoon vegetable oil, then add the steak; sear 3 minutes per side. Transfer the skillet to the oven and cook until a meat thermometer inserted sideways into the steak registers 135 degrees F for medium rare, 15 to 20 minutes. Transfer the steak to a cutting board.
Meanwhile, heat the remaining 2 tablespoons vegetable oil in a medium skillet over medium heat. Add the onion and garlic and cook, stirring, until soft, 5 minutes. Add the collard greens and 1/2 cup water and cook, stirring occasionally, until warmed through, 10 minutes. Add 1 tablespoon vinegar, and salt and pepper to taste.
Whisk the ketchup, the remaining 3 tablespoons vinegar, the honey, Worcestershire sauce, mustard and 1/2 cup water in a bowl. Return the cast-iron skillet to medium-high heat; add the ketchup mixture and cook until thickened, 3 to 5 minutes. Slice the steak against the grain. Serve with the sauce and collard greens.