In a large mixing bowl, combine 2 cups of the flour with the sugar, yeast and salt. In a separate microwave-safe bowl, warm the milk to about 110°F (just warm to the touch, not hot), add the melted butter, then whisk in the eggs. Pour this wet mixture into the dry ingredients and stir until combined.
Add the remaining flour gradually, stirring until the dough forms a soft ball. Turn onto a floured surface and knead for 5-7 minutes until smooth and elastic. The dough should spring back when lightly pressed with your finger.
Place the dough in a lightly greased bowl, cover with plastic wrap or a damp towel, and let rise in a warm place for about an hour, or until doubled in size.
While the dough rises, make your filling. Toss the diced apples with brown sugar, cinnamon, nutmeg, and cornstarch. The cornstarch is crucial here—it will absorb excess moisture from the apples during baking, preventing soggy rolls.
After the first rise, punch down the dough and roll it out on a floured surface into a large rectangle, approximately 18x12 inches. Brush the surface with melted butter, then evenly spread the apple filling mixture, leaving a 1-inch border along one long edge.
Starting with the long edge (opposite from the border), tightly roll the dough into a log. Pinch the seam to seal. Using unflavored dental floss or a sharp knife, cut the log into 12 equal pieces, each about 1.5 inches thick.
Arrange the rolls in a greased 9x13 inch baking dish, spacing them evenly. Cover tightly with plastic wrap and refrigerate overnight (8-12 hours).
The next morning, remove the rolls from the refrigerator and let them sit at room temperature for 45-60 minutes to take the chill off. Preheat your oven to 350°F and bake for 25-30 minutes, until golden brown.
While the rolls are baking, beat together the cream cheese and butter until smooth. Add powdered sugar and vanilla, mixing until combined. Add milk gradually until you reach your preferred consistency.
Let the rolls cool for 5-10 minutes before spreading the glaze over the warm (not hot) rolls. This allows the glaze to partially melt into the crevices while still maintaining some thickness on top.