Preheat oven to 400°F.
Place steaks on a lined baking sheet. Season both sides with salt and pepper and drizzle with olive oil. Put Broccolini in a mixing bowl and toss with ½ tablespoon sesame oil. Add to baking sheet.
Place mushrooms in the mixing bowl and toss with remaining sesame oil and garlic. Add mushrooms to baking sheet, making sure nothing is overlapping. Sprinkle vegetables with salt. Bake for 12-15 minutes or until steak reaches desired level of doneness with a minimum internal temperature of 120-125°F for rare. Remove from oven and allow to rest for 5 minutes before slicing and serving.