Combine first 3 ingredients in container of an electric blender; cover and process until smooth. Add lime juice and sugar; cover and process until smooth. Stir in lime zest.
Divide mixture in half. Stir Spicy Southwest Chile Oil into one half of sauce mixture. Add shallots, mint, green onions, and gingerroot to remaining half of sauce mixture. Set aside.
Sprinkle steak evenly with 1/2 teaspoon pepper and salt. Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Place steak on rack; grill, covered, 8 minutes on each side or to desired degree of doneness. Remove steak from grill; let stand 5 minutes. Slice steak diagonally across the grain into 1/4-inch-thick slices; cut slices into 1/4-inch-thick strips. Combine steak strips and shallot mixture; cover and chill thoroughly.
Combine mixed greens and oil mixture; toss well. Arrange on salad plates; top with steak strip mixture. Sprinkle with cilantro and red pepper.