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Heat 1 teaspoon oil in a medium skillet over medium heat. Add the bell peppers and onion and cook, stirring occasionally, until softened and just beginning to brown, about 10 minutes. Add the garlic and cook, stirring, until fragrant, about 1 minute. Remove from the heat.
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Meanwhile, heat the remaining 1 teaspoon of olive oil in another medium skillet over medium low heat. Add the corn and cook, stirring occasionally, until hot and just beginning to brown, about 8 minutes. Add the lime juice and salt and pepper to taste. Remove from the heat.
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Spritz a griddle or large skillet with olive oil and preheat on medium high heat. Once hot, add 3-4 corn tortillas in a single layer (or fewer if you need to work in batches to get them to fit). Top the tortillas evenly with the pepper mixture, corn, and cheese. Top each tortilla with another tortilla and spritz the top with olive oil. Allow to cook until crispy and brown on the bottom, about 5 minutes. Carefully flip the quesadillas and allow to cook until crispy and brown on the other side and melty and hot in the middle, another 5 minutes.
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Transfer the quesadillas to a plate, cut into fourths, and top with additional peppers, cilantro, green onion, and a drizzle of yogurt.