1. Fry bacon strips in 10-inch nonstick skillet over medium heat until crisp, about 5 minutes. Using slotted spoon, transfer bacon to paper towel-lined plate; pour fat into small bowl and reserve, if desired. Wipe out skillet with paper towels.

2. Heat skillet over medium heat until hot, about 2 minutes. Place 1 tortilla in skillet and toast until soft and puffed slightly at edges, about 2 minutes. Flip tortilla and toast until puffed and slightly browned, 1 to 2 minutes longer. Slip tortilla onto cutting board. Repeat to toast second tortilla while assembling first quesadilla. Sprinkle 1/3 cup cheese, half the bacon, 1 tablespoon scallions, and half of jalapeños, if using, over half of tortilla, leaving 1/2-inch border around edge. Fold tortilla in half and press to flatten. Brush surface generously with oil or bacon fat, sprinkle lightly with salt (omit if using bacon fat), and set aside. Repeat to form second quesadilla.

3. Place both quesadillas in skillet, oiled sides down; cook over medium heat until crisp and well browned, 1 to 2 minutes. Brush surfaces with oil or bacon fat and sprinkle lightly with salt. Flip quesadillas and cook until second sides are crisp and browned, 1 to 2 minutes longer. Transfer quesadillas to cutting board; cool about 3 minutes, halve each quesadilla, and serve.

To cook two quesadillas at once, arrange folded edges toward center of skillet.