Heat 3 tablespoons oil in large skillet over high heat and cook steak, in batches, turning once, until desired doneness, about 1 minute. (Be sure not to overcook so steak stays juicy.) Remove steak and set aside.
Heat remaining 1 tablespoon oil in same skillet over medium-high heat and cook onions, stirring occasionally, until very soft and golden, about 8 minutes. Stir in poblano pepper and garlic and cook about 1 minute.
Stir in water, cilantro and remaining 1/2 tablespoon Bouillon and cook, about 1 minute. Remove from heat and set aside.
Slice steak. Heat 1 tortilla in large nonstick skillet over medium-high heat 1 minute. Place 1/4 of the sliced steak, then 1/4 of the onion mixture and 1/4 of the cheese on one half of the tortilla. Fold the other half of the tortilla over the filling.
Cook over medium-high heat, pressing down with a spatula, until bottom is lightly browned. Carefully turn quesadilla and cook until lightly browned and cheese is melted, about 2 minutes. Remove quesadilla and keep warm. Repeat with remaining ingredients.