In a large bowl, using an electric mixer fitted with a whisk attachment, stir together the milk, sugar, and yeast to combine. Then, let the mixture sit for 5 to 10 minutes, or until the surface starts to get foamy.
Add the eggs, melted butter, salt, maple syrup, cinnamon, and nutmeg, and whisk just until combined. Then, replace the whisk attachment with a dough hook and add 1 cup (135 g) of the flour and mix on low speed until combined.
Gradually add 3 more cups (405 g) of the flour and knead the dough slowly and increase the speed to medium and then high after about 10 seconds on each level. Knead for 5 to 10 minutes on high speed. The dough should be slightly sticky to the touch but should start to come away from the sides of the bowl after a few minutes of kneading. If it continues to stick to the sides of the bowl after a few minutes of kneading, add 1 tablespoon (8 g) of flour at a time (up to ½ cup [67 g] in total) and mix on low speed until the dough is of the right consistency; then, turn the speed back to high. Do not add more than ½ cup (67 g) of flour, or the rolls will be dry. In the end, the dough should be smooth, soft, and lightly sticky, and the bowl should be clean without any dough on the sides.
Lightly spray a large, heatproof bowl with nonstick spray and transfer the dough to the bowl; lightly oil the top of the dough as well. Then cover with a clean and dry kitchen towel and let rest for 15 minutes.
Meanwhile, prepare the filling. In a small bowl, stir together brown sugar and cinnamon. Set aside.
Preheat the oven to 200°F (100°C). Line a baking sheet with parchment paper and set aside.
On a very lightly floured surface (use as little flour as possible to keep the dough from sticking to the rolling pin or surface), roll out the dough into a 20 x 18-inch (50 x 45 cm) rectangle. Spread the butter all over the rolled dough and sprinkle with the sugar mixture evenly. Starting at a long side, roll up the dough tightly. Cut into 12 equal-sized rolls and transfer to the prepared baking sheet, about 2 inches (5 cm) apart. Turn off the preheated oven and place the baking sheet inside, leaving the oven door ajar, for 20-30 minutes, or until the rolls are doubled in size.
Then, remove the baking sheet from the oven and preheat to 375°F (190°C).
Bake for about 20-25 minutes until lightly browned. After 10-15 minutes of baking, cover loosely with aluminum foil to prevent heavy browning if needed.
While the rolls are baking, prepare the frosting. Therefore, in a medium mixing bowl, using a handheld or stand mixer fitted with a whisk attachment, beat the butter until creamy, about 1-2 minutes. Add the cream cheese and mix until smooth, creamy, and no lumps remain. Add the powdered sugar and mix to combine. Then stir in the vanilla and mix until creamy for about 1 minute.
Remove the rolls from the oven, let cool for 5-10 minutes. Then spoon the frosting on top of the rolls when they are still warm and spread evenly. They will stay fresh and soft in an airtight container in the refrigerator for up to 3 days. Reheat leftover rolls in the microwave for about 20-30 seconds before serving. Freeze for up to 2 months.