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Heat large skillet coated with oil on medium-high heat.
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When oil is shimmering, sauté mushrooms (and jalapenos, if using) until soft and beginning to brown, about 5 minutes. Season with pepper and garlic powder as they cook.
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Remove mushrooms to bowl, and salt them.
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Wipe out skillet, coat with fresh oil and heat over medium heat.
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When oil is heated, place corn tortilla in pan. Cover tortilla generously with cheese.
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Add 2 tablespoons of mushrooms and some chopped cilantro. Sprinkle more cheese over mushrooms and cilantro.
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Once cheese starts melting, place second tortilla on top and press down lightly.
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Cook on first side until bottom is golden brown and edges are beginning to crisp, then flip with large spatula and continue to cook until tortilla is toasted and cheese is melted.
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Remove from pan to a warm plate and cover as you repeat steps with remaining tortillas. Quarter or halve each quesadilla and serve immediately with sides of your choice.