Preheat a large skillet over medium-high heat. When hot add chorizo, breaking up into smaller pieces with a wooden spoon. Cook about 5-7 minutes, stirring occasionally, until browned and fully cooked through. Transfer with a slotted spoon to a large bowl.

In the same pan, add shiitake mushrooms and cook undisturbed until deep golden brown on first side, about 4 minutes. Add shallots, then stir mushrooms and continue cooking until evenly browned on both sides, another 3-4 minutes. Season with salt, then transfer to the bowl with chorizo. Add sage and parmesan then toss to combine.

Wipe out pan, then coat with nonstick spray and heat over medium. Meanwhile, lay tortillas out on a cutting board. On half of each tortilla spread an equal amount of fig jam in a thin layer. Add about 2 Tbsp of grated cheese, then top with equal portions of chorizo mixture. Top with an additional 2 Tbsp of grated cheese, then fold tortilla over onto itself. Carefully transfer to heated pan.

Cook about 3-4 minutes per side, or until tortilla has browned and cheese is melted. Slice each quesadilla into 3 equal pieces. Serve immediately.