Heat a large nonstick skillet with EVOO over medium-high heat. Add the chorizo, sage, thyme, salt and freshly ground black pepper. Cook until the chorizo is brown and slightly crispy. Add the turkey, deglaze the pan with the white wine and continue to cook until all the liquid cooks out and the turkey is heated through.
Remove to a bowl and reserve.
Return the skillet to medium-high heat with a drizzle of EVOO. Add a tortilla to the pan and blister on one side.
Flip it over and cover half evenly with cheese.
Add some of the turkey and onion mixture on top of the cheese.
Fold the other side of the tortilla over the top of the filling and gently press down with a spatula. Cooked the filled quesadilla for 30 seconds to a minute longer on each side to lightly brown and crisp the quesadilla and melt the cheese. Remove the quesadilla to a large cutting board or transfer to a warm oven to hold, and repeat with the remaining quesadilla ingredients.