Umami is essentially the fifth taste bud sensation we can taste, once hidden away during our elementary learnings of youth. It's description is that of a "savory" nature... like a nice, meaty, broth-like yum. The most classic example is the shiitake mushroom. It's not sweet, sour, salty or bitter. It's got this... other flavor... this umami flavor.
Based on that, I can only guess that this special sauce incorporates a lot of foods rich in umami flavors. If I were to make this sauce, it'd probably be a mix of extra ripe tomatoes, shiitake mushrooms and some kind of beefy bouillon powder. Maybe replace the tomatoes with something more like a ketchup, but homemade of course.
Speaking of special ketchup, have you ever tried curry powder in ketchup? Pretty tasty.
Related Link: Google Trending "Umami Burger"