Preheat your oven to 400 degrees Fahrenheit and line a baking sheet with parchment paper.
Place the asparagus on the sheet, drizzle with half the olive oil, and sprinkle with a pinch of the sea salt and black pepper.
Roast the asparagus for 12 to 15 minutes until it is tender and slightly charred at the tips.
Pat the rump steak dry with paper towels and season both sides generously with the remaining sea salt and black pepper.
Heat a cast-iron skillet over medium-high heat with the remaining olive oil until shimmering.
Place the steak in the pan and sear for 3 to 4 minutes without moving it to develop a deep brown crust.
Flip the steak, then add the minced garlic, rosemary, and thyme to the pan, tilting it to baste the meat with the infused oil.
Cook for another 3 minutes for medium-rare, then remove the steak from the pan and let it rest on a cutting board for 5 minutes.
Slice the steak against the grain and serve alongside the roasted asparagus with a fresh squeeze of lemon juice.