In a medium non-stick skillet heat 1 tablespoon oil over medium-high heat. Saute the shallot until fragrant, about one minute. Add the broccoli and cook until vibrant green, about 2 minutes. Add 2 tablespoons water and continue to cook, stirring occasionally, until the florets are tender, about 3 minutes more. Season with salt and the chili poweder. Remove the broccoli to a medium mixing bowl and wipe out the skillet.

Add the cheese to the mixing bowl and stir to combine. The cheese will start melting, so make sure it doesn't clump too much.

On a cutting board, arrange three of the tortillas. Divide the broccoli mixture between them, spreading to form an even layer. Top with the remaining tortillas.

Brush the skillet with oil. Pan fry the quesadillas over medium-high heat until golden brown and the cheese is starting to ooze out the sides, about 2 minutes per side. Remove to a baking sheet. Keep the quesadillas warm in the oven until ready to eat or cut into four wedges and serve immediately.