In a large mixing bowl or the bowl of a stand mixer, whisk together the flour, instant potato flakes, sugar, salt, and yeast.
Set the whisk aside and switch to a sturdy wooden spoon. Stir in the milk, butter, egg, and finely grated carrot until a shaggy dough forms.
Knead the dough by hand or by stand mixer fitted with a dough hook for 8 to 10 minutes, or until you have a smooth and elastic dough. Place dough in a clean bowl, cover with a damp tea towel, and set aside to rise in a warm, draft-free place until nearly doubled in bulk and puffy, about an hour or so.
Spray a 9-inch by 13-inch baking pan with nonstick cooking spray. Set aside.
In a small mixing bowl, use a fork to toss together the sugars, cinnamon, ginger, nutmeg, and cloves. Use the same fork to start squishing the butter into the sugar mixture. When it is mostly incorporated, switch to a spatula to cream the mixture together until even in colour and texture.
Roll the dough out to a rectangle that is approximately 12-inches by 15-inches. Spread the butter and sugar mixture evenly over the rectangle, leaving 1-inch of one long edge free of the mixture.
Starting at the long edge that has butter, roll it up jelly-roll style. Pinch together the seams.
Cut the roll of dough into 12 equal pieces. Arrange in the prepared pan in 4 rows of 3. Cover the dough loosely with plastic wrap.
Preheat the oven to 375°F while the dough rises until double in bulk, about 20 to 30 minutes. Remove the plastic wrap and bake for 25 minutes or until the center rolls measure 190°F on an instant read thermometer. Cool for 15 minutes.
While the rolls cool, use a hand mixer, stand mixer, or sturdy spoon to mix the cream cheese and butter, together until fluffy and even.
Beat in the powdered sugar and extract ‘til smooth, then spread over the cooled rolls. Store leftovers, tightly wrapped, at room temperature.