Heat the olive oil in a large nonstick skillet over medium heat. When the oil is hot and shimmering, add the butternut squash and Brussels sprouts. Cook until very tender and lightly browned in spots, about 18-20 minutes. Stir in the paprika, chili powder, salt, and cayenne and cook for 1 minute to toast the spices. Transfer the butternut and Brussels to a bowl and briefly set aside.
Crack the eggs into a mixing bowl and whisk vigorously until pale yellow and slightly frothy.
Wipe out the skillet and return it to the stove over medium-low heat. Place a plate or bowl next to the stove. (If your pan is not truly nonstick, spray it with cooking spray or add a little olive oil or butter to the pan to prevent the eggs from sticking!!) When hot, pour in the beaten eggs. Cook, stirring in big sweeping motions with a spatula to form large curds, until the eggs are just set. (This will take a couple minutes MAX, so be sure to have that plate/bowl ready.) Transfer the eggs to the plate/bowl.-Assembly time! For each dilla: Sprinkle a ¼ cup of cheese on one half of the tortilla. Add a quarter of the butternut and Brussels mix, a quarter of the scrambled eggs, and 1 tablespoon of scallions. Sprinkle with another ¼ cup cheese and fold the empty half the tortilla over the filling to close.
Wipe out the pan one last time and return it to the stovetop over medium heat. When hot, add two quesadillas to the pan and cook for 2 to 3 minutes or until the underside of each tortilla is lightly browned and crispy. Flip them carefully and cook for another 2 minutes on the opposite side, then transfer to a cutting board. Repeat this process with the remaining queadillas.
Slice each quesadilla into 3 (or 4) triangles and serve warm. Feel free to get some hot sauce, sour cream, or salsa involved. You must always do you.