For the Crepes, mix flour, cornstarch and sea salt in large bowl with wire whisk. Gradually add water, whisking until batter is very smooth. Whisk in sesame oil. (Batter will be thin.) Let stand while preparing filling.
For the Fajita Filling, mix lime juice, 1 tablespoon of the oil, honey, garlic powder, sea salt and pepper in small bowl. Reserve 2 tablespoons marinade in bowl. Pour remaining marinade over steak in large resealable plastic bag; turn to coat well. Refrigerate 30 minutes or longer for extra flavor.
Heat remaining 2 tablespoons oil in large skillet on medium-high heat. Add steak; cook 3 minutes per side or until evenly seared. Remove from pan and place on cutting board.
Reduce heat to medium. Add sliced onion and chile pepper to skillet; cook 2 to 3 minutes or until softened. Stir in tomatoes, reserved marinade, ancho chile pepper and cumin. Bring to boil. Cook 5 to 6 minutes or until slightly thickened.
Slice steak across the grain into thin strips. Return to pan with tomato mixture. Keep warm.
To cook the crepes, brush about 1/2 teaspoon of the oil in 12-inch nonstick skillet on medium-low heat. Pour about 1/3 cup of the batter into skillet, tilting to evenly cover bottom of skillet. Cook 2 to 3 minutes or until bottom of crepe begins to brown.
Lightly beat 1 egg in small bowl then pour over crepe in pan in even layer to cover crepe. Continue to cook 1 to 2 minutes or until egg is just set. Using a flexible spatula, carefully turn crepe over. Cook 2 to 3 minutes or until crepe is lightly browned and crispy. Place crepe, egg side down, on cutting board. Repeat with remaining batter and eggs.
To assemble, spoon 1 cup of the Fajita Filling and 1/4 each of the shredded cheese, avocado and cilantro down the center of the non-egg side of each crepe. Fold or roll crepe to enclose filling. Serve immediately with lime wedges.