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Preheat broiler to high.
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Place poblanos on baking sheet and char under the broiler until skin blackens on all sides, 7 to 8 minutes.
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Place in a bowl cover with towel or plastic wrap; let stand 10 minutes. Peel and seed the peppers, then slice.
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Heat 1 tbsp olive oil in large skillet over medium heat, add onion and cook for 4-5 minutes, till onion tender. Remove from skillet.
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In the same skillet over medium-high heat add a drizzle of extra-virgin olive oil; add a tortilla, cover the tortilla with half the cheese, poblano, onion and cilantro.
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Fold the tortilla in half and cook 2 minutes to crisp and char the tortilla evenly and melt cheese. Remove and cut into wedges; repeat.