Preheat oven to 220C fan-forced. Place pumpkin and onion in a small roasting pan. Season with salt and pepper, drizzle with 2 tablespoons oil and toss to combine. Roast, stirring halfway, for 20 minutes or until pumpkin is light golden and tender. Remove from oven and cool in pan for 10 minutes. Turn off fan function on oven and reduce heat to 200C.
Transfer pumpkin to a bowl. Crumble over goat's cheese, then add jarlsberg, chilli, oregano and paprika. Using a fork, stir gently to combine.
Place 3–4 tortillas on an oven tray and bake for 1 minute or until softened and pliable. Working quickly with 1 tortilla at a time, brush around edge with eggwash, then place 1/4 cup pumpkin mixture on one half, leaving a 1cm border. Fold tortilla in half and press edges together firmly (don't worry if they come slightly apart). Repeat process with remaining tortillas, eggwash and pumpkin mixture.
Line 2 oven trays with baking paper. Divide quesadillas among trays. Brush both sides with remaining 60ml (1/4 cup) oil, then brush tops lightly with egg wash. Scatter with pepitas. Season with salt. Bake for 15 minutes or until golden.
Place on a platter to serve.