In a small bowl, combine the thinly sliced apples, brown sugar, ground cinnamon, and ground nutmeg. Toss gently until the apple slices are fully coated.

Lay the two tortillas on a clean, flat surface. Spread 2 oz of softened cream cheese evenly over each tortilla. Arrange the coated apple slices in a single layer on one half of each tortilla.

Fold the empty half of each tortilla over the apple filling to create a half-moon shape. Melt the butter in a large non-stick skillet over medium heat. Once the butter is sizzling, carefully place the quesadillas in the skillet.

Cook for 2-3 minutes on each side, until the tortillas are golden brown and crispy, and the filling is warm and gooey. Remove from the skillet, let rest for a minute, then slice in half and serve immediately.