Add the warm milk (115ºF) to the bowl of a stand mixer. Sprinkle the yeast over the milk and leave it undisturbed for 3–4 minutes. A little foam should develop as the yeast activates.
Add the room-temperature eggs, butter, and sugar. Mix until everything is incorporated.
Add the salt and 4 cups of the flour, reserving the remaining 1/2 cup. Using the beater attachment, mix only until the ingredients have barely come together. Leave the mixture to rest for 5 minutes so the flour can absorb the liquid.
Scrape any dough from the beater, remove the beater attachment, and replace it with the dough hook.
Knead on medium speed for 5–7 minutes. If necessary, gradually add some of the reserved 1/2 cup flour until a dough forms. The finished dough should be smooth and elastic while remaining tacky. It should pull away from the sides of the bowl but may still cling slightly to the bottom. Avoid adding excess flour. About 4 1/4 cups is generally enough, although you should begin with 4 cups.
Coat a large bowl with cooking spray. Using a rubber spatula, transfer the dough into the prepared bowl. Cover it with a towel or wax paper.
Put the bowl somewhere warm and allow the dough to rise until doubled, usually about 30 minutes. One option is to run the oven at its lowest temperature for 1–2 minutes, switch it off, and then place the covered dough inside. Avoid letting the dough rise excessively, which can make the finished rolls too airy.
While the dough rises, make the filling. Mix the softened butter, brown sugar, and cinnamon together in a medium bowl until evenly combined. Set aside.
Generously flour a pastry mat or work surface. Place the risen dough on it and dust the top of the dough with additional flour.
Flour your rolling pin, then roll the dough into approximately a 24×15-inch rectangle. The dimensions do not need to be exact.
Using a rubber spatula, spread the cinnamon filling evenly across the entire rectangle of dough.
Beginning with one of the long edges, tightly roll the dough into a log, jelly-roll style.
Divide the log into 12 slices and arrange them in a greased 9×13-inch baking pan. Cover the pan and let the rolls rise for 20 minutes while the oven preheats.
Preheat the oven to 375ºF.
Gently warm the heavy cream just enough to remove the refrigerator chill. It should feel warm, not hot. Once the rolls have finished rising, pour the 1/2 cup heavy cream over them, letting it flow between and around the rolls.
Bake for 25 minutes, or until the rolls are lightly golden and the rolls in the center are cooked through. Baking time can vary according to the size of the rolls, the pan being used, and how closely they are arranged. They may require as long as 30 minutes. Begin checking at 20 minutes; if the tops are browning too quickly, loosely cover the pan with foil for the remainder of the baking time.
While the baked rolls cool, prepare the frosting.
Put the softened cream cheese and butter in a large bowl. Beat together with a hand mixer until thoroughly blended.
Add the maple extract (or vanilla) and powdered sugar. Beat until smooth and combined.
Spread the cream cheese frosting over the cooled cinnamon rolls.