Preheat oven to 325. Place a wire rack into a roasting pan, and fill the bottom of the pan with about ½ an inch water, just so that the bottom is covered.
Pat the flat iron steaks dry with a paper towel, then pat the flat iron steaks with olive oil and drizzle on the balsamic vinegar, then sprinkle seasonings onto the flat iron steaks and lay on the wire rack in the roasting pan. Bake for 20 minutes, remove from oven, allow to rest for 10 minutes, then slice and place on top of the salad.
While the steak is baking make the vinaigrette by simply whisking all the ingredients together. Also prepare the salad by putting the lettuce, spinach, mozzarella and cherry tomatoes in a bowl.
To assemble the salad place steak on top of salad, and then gently pour vinaigrette over, or let everyone dress their own salad.