In a small bowl, combine the coconut sugar, cinnamon, nutmeg, and ginger, then remove 1/4 cup of the mixture and set the remainder aside.
Melt 1 tablespoon of butter in a large skillet over medium-high heat, then add the chopped apples and 1/3 cup water and sauté for 1 to 2 minutes.
Sprinkle the reserved 1/4 cup sugar-spice mixture over the apples and cook for another 1 to 2 minutes, until the sugar melts and the apples are slightly tender but still hold their shape.
Transfer the apple mixture from the skillet and let it cool completely before assembling the rolls.
In a large mixing bowl, combine 2 cups of flour with the instant yeast and salt.
Add the warm milk, warm water, maple syrup, and oil, then mix until the dough mixture is smooth and evenly combined.
Knead in the remaining flour a little at a time until a soft, slightly tacky dough forms, taking care not to add more flour than needed.
Cover the dough and let it rest in a warm place for 5 minutes.
Place the dough on a lightly floured surface and roll it into a large, evenly thick rectangle.
Spread the softened butter evenly over the dough, leaving a narrow border around the edges.
Sprinkle the remaining coconut sugar and spice mixture over the butter, then distribute the cooled apples evenly across the dough.
Starting from one long edge, roll the dough into a snug log and place it seam-side down.
Cut the log in half with a sharp knife or unflavored dental floss, then divide each half into six equal rolls.
Arrange the 12 rolls in a greased or parchment-lined 13x9-inch baking dish.
For same-day baking, cover the pan and let the rolls rise in a warm place for about 30 minutes, until puffy and beginning to touch.
For overnight rolls, cover the shaped pan tightly with foil and refrigerate overnight, then let the rolls rise in a warm place for 30 to 60 minutes the next morning, until puffy.
Preheat the oven to 350°F near the end of the rising time.
Bake the rolls on the middle oven rack for 25 to 35 minutes, until the edges are lightly golden and the center rolls are puffed and fully cooked.
Remove the pan from the oven and let the rolls cool slightly before frosting.
Beat the softened cream cheese and butter together until smooth, then blend in the maple syrup, vanilla extract, and cinnamon.
Add milk 1 teaspoon at a time only if needed to make the frosting easier to spread.
Spread the cinnamon cream cheese frosting over the warm rolls and serve.