Take the T-bone steaks out of the refrigerator and let them come to room temperature for about 30 minutes. This helps them cook evenly. Season both sides generously with salt and black pepper.

In a bowl, combine the chopped oregano and garlic chips. Press this mixture firmly onto the top of each steak to create a crust.

Heat a large skillet over medium-high heat and drizzle with olive oil. Once the oil is hot, add the T-bone steaks, crust side down. Sear for about 4-5 minutes or until a nice crust forms. Flip the steaks and cook for an additional 4-5 minutes for medium-rare, or adjust the time to your preferred doneness. Remove the steaks from the skillet and let them rest for at least 5 minutes.

In the same skillet used for the steaks, reduce the heat to medium. Add the butter and let it melt, swirling occasionally until it turns a light brown color and has a nutty aroma. Add the chopped shallots and sauté for about 2-3 minutes until they are translucent.

Carefully pour in the balsamic vinegar, scraping up any browned bits from the bottom of the skillet. Let it simmer for another 2 minutes until slightly thickened.

Slice the T-bone steaks and arrange them on a platter. Drizzle the brown butter and balsamic-shallot infusion over the steaks. Garnish with additional oregano leaves if desired. Serve immediately.