1. Cook the bacon in a medium skillet over medium-high heat until crisp, about 8 to10 minutes. Transfer the bacon to a paper towel-lined plate and discard all the pan drippings.
2. Add 1 teaspoon butter and the shallots and cook until brown, 2 to 3 minutes. Add the asparagus to the skillet and season with salt and pepper. Cook until the asparagus are bright green and tender; about 2 minutes. Set aside.
3. Spread a thin layer of cheese over a tortilla and scatter a quarter of the herbs on top. Place the tortilla cheese-side up in the skillet. Scatter a quarter of the bacon and asparagus on the lower half of the tortilla, then fold the tortilla over and press lightly. Cook until golden brown, turning once, about 3 minutes on each side. If the pan gets dry, add butter, as needed. Repeat with remaining ingredients. Cut quesadillas into wedges and serve.
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