Preheat oven to 375F.
Rub the inside of each cup of a 6-cup muffin tin with butter and set aside.
In a medium-size mixing bowl, whisk together the eggs, milk, cinnamon, vanilla and nutmeg.
Cut a slit in the corner of each slice of bread from the middle of the slice to the edge. Dip each slice of bread in the egg mixture then lightly press it into a cup of the muffin tin, overlapping the pieces where you cut the slit to make it fit into the cup without tearing.
Bake the French toast cups for 12-14 minutes, until they're light golden brown.
While the cups are working, place a small saucepan over medium-low heat with the maple syrup and cinnamon stick. Keep the syrup warm and stir it occasionally while finishing up everything else.
Place a medium skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the sausage and saute, breaking it up with a wooden spoon, until golden brown and cooked through, 8-10 minutes. Add the chopped apples and fresh cider to the pan and saute until softened, 3-4 minutes.
Allow the cups to cool slightly in the muffin tin before removing them. To serve, arrange the cups on a platter, fill each one with the apple sausage mixture and drizzle with cinnamon maple syrup.