Preheat oven to 400°F (200°C).
On a large rimmed baking sheet, toss the halved Brussels sprouts and cubed butternut squash with 2 tablespoons of olive oil, 1 teaspoon of salt, and 0.5 teaspoon of pepper.
Spread the vegetables in a single layer and roast for 25-30 minutes, tossing halfway through, until tender and browned at the edges.
Pat steaks dry with paper towels and season both sides generously with remaining salt and pepper.
Heat a heavy cast-iron skillet over medium-high heat with the remaining 1 tablespoon of olive oil until the oil begins to smoke slightly.
Place steaks in the skillet and sear for 3-4 minutes per side for medium-rare, or until desired internal temperature is reached.
Reduce heat to medium and add the butter, minced garlic, rosemary, and thyme to the skillet.
Tilt the pan and use a large spoon to continuously baste the steaks with the foaming garlic butter for 2 minutes.
Remove steaks from the skillet and allow to rest on a warm plate for 5-7 minutes.
Serve the steaks alongside the roasted vegetables, drizzling remaining garlic butter from the pan over the meat and vegetables.