Remove the ribeye steak from the refrigerator and let it come to room temperature for about 20 minutes.
Preheat the oven to 425°F. Toss the broccoli florets with 1 teaspoon of olive oil, a pinch of salt, and pepper, then spread them on a baking sheet.
Roast the broccoli in the oven for 15-20 minutes until tender and slightly charred.
Meanwhile, pat the ribeye dry with paper towels and season generously with salt and black pepper on both sides.
Heat a heavy skillet over medium-high heat and add the remaining 1 teaspoon of olive oil.
Add the ribeye steak to the skillet along with the garlic cloves (smashed with the side of a knife) and the fresh rosemary and thyme sprigs.
Sear the steak for about 3-4 minutes on each side for medium-rare, or adjust cook time to your desired doneness, spooning the infused oil over the steak as it cooks.
Once cooked, transfer the steak to a plate and let it rest for 5 minutes before slicing.
Serve the sliced ribeye alongside the roasted broccoli, drizzling any pan juices over the top for extra flavor.