Remove the top sirloin steaks from the refrigerator and let them sit at room temperature for about 30 minutes. Season both sides generously with coarsely ground salt and pepper.
In a cast iron skillet, heat the vegetable oil over medium-high heat. You want the oil to shimmer but not smoke.
Once the oil is hot, carefully place the seasoned steaks in the skillet. Sear for about 4-5 minutes on one side without moving them, allowing a nice crust to form.
Flip the steaks and add 2 tablespoons of butter, the rosemary sprig, and the whole garlic cloves to the pan. Cook for an additional 4-5 minutes for medium-rare, basting the steaks with the melted butter and pan juices.
Use a meat thermometer to check the internal temperature. For medium-rare, aim for 130°F. Adjust cooking time as needed based on your preferred doneness.
Once cooked to your liking, remove the steaks from the skillet and transfer them to a plate. Tent with foil and let them rest while you prepare the sauce.
In the same skillet, reduce the heat to medium and add the minced shallot and the minced garlic. Sauté for about 1-2 minutes until fragrant and softened.
Pour in the low sodium chicken broth, scraping the bottom of the pan to release any delicious browned bits. Let it simmer for a couple of minutes.
Stir in the heavy cream, balsamic vinegar, Dijon mustard, chives, and parsley. Cook for another 2-3 minutes until the sauce thickens slightly. Finish with 1 tablespoon of butter for a rich, glossy finish.
Slice the rested steaks against the grain, place them on a serving platter, and drizzle the balsamic herb cream sauce over the top. Garnish with additional herbs if desired.