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Combine 2 teaspoons of the brown sugar, the chili powder, cumin, pepper, and salt in a small bowl.
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Spray a small saucepan with nonstick spray and heat over medium-low. Add the onion and cook, stirring frequently, until softened, about 4 minutes.
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Add 1 tablespoon of the spice mixture, the remaining 1 tsp of brown sugar, the ketchup, water, steak sauce, and Worcestershire sauce; bring to a boil.
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Reduce the heat and cook, covered, stirring occasionally, until the flavors are blended, 10 minutes.
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Set aside and keep warm.
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Spray the grill rack with nonstick spray and heat the grill to medium-high or prepare a medium-hot fire.
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Rub the steaks with the remaining spice mixture.
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Place on the grill rack and grill until an instant-read thermometer inserted into the side of each steak registers 130 degrees, 3-4 minutes on each side.
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Transfer to a platter, cover loosely with foil and let stand 5 minutes (until the temperature increases to 135 degrees for medium-rare).
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Serve with the sauce.