Preheat oven to 400°F (200°C).
Toss broccoli florets with olive oil, salt, and pepper. Spread on a baking sheet.
In a skillet over medium-low heat, add olive oil and sliced red onions. Cook slowly for 20–30 minutes until deeply softened and caramelized, stirring occasionally.
Optional: Add balsamic vinegar and sugar during the last 5 minutes. Season with salt and pepper.
Roast broccoli in the oven for 15–20 minutes, until tender-crisp and slightly charred.
2. Prepare the Steak
Pat the T-Bone steak completely dry with paper towels.
Season generously on both sides with salt and freshly ground black pepper.
3. Sear the Steak
Heat a heavy-bottomed skillet (cast iron recommended) over medium-high heat until smoking. Add olive oil.
Carefully place the steak in the skillet and sear 3–5 minutes per side for medium-rare, adjusting for your preferred doneness.
Optional: In the last minute of cooking, add butter and fresh herbs, basting the steak with the melted butter.
