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Heat 10-inch nonstick skillet over medium-high heat until hot, about 2 minutes.
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Add corn and cook, stirring occasionally, 3 to 5 minutes; transfer corn to medium bowl.
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Heat 2 teaspoons vegetable oil add red onion and cook, stirring occasionally, about 3 minutes.
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Add garlic and chili powder and cook 1 minutes; stir in beans and cook about 1 minute.
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Return corn to skillet and toss to combine; press mixture with spatula to lightly crush black beans.
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Transfer mixture to empty bowl, stir in lime juice, and season to taste with salt.
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Wipe out skillet with paper towels and return pan to medium heat until hot, about 2 minutes.
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Place 1 tortilla in skillet and toast about 2 minutes. Flip tortilla and toast 1 to 2 minutes longer. Slip tortilla onto cutting board.
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Repeat to toast second tortilla while assembling first quesadilla.
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Sprinkle 1/3 cup cheese, half the corn and bean mixture, and half of jalapeños, if using, over half of tortilla, leaving 1/2-inch border around edge.
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Fold tortilla in half and press to flatten.
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Brush surface generously with oil, sprinkle lightly with salt, and set aside. Repeat to form second quesadilla.
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Place both quesadillas in skillet, oiled sides down; cook over medium heat until crisp and well browned, 1 to 2 minutes.
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Brush surfaces with oil and sprinkle lightly with salt.
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Flip quesadillas and cook until second sides are crisp and browned, 1 to 2 minutes longer.
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Transfer quesadillas to cutting board; cool about 3 minutes, halve each quesadilla, and serve.