In a large bowl or mixer, add the warm milk, softened butter, eggs, sugar, yeast, coconut extract, salt, and flour. If using a stand mixer, mix on low speed for 10 minutes. If you're mixing by hand, mix the dough until it comes together. Transfer to a floured surface and knead for 10-12 minutes or until a smooth ball is formed.
Place the dough into an oiled or buttered bowl and cover with plastic wrap. Let the dough sit in a warm place to rise for 1 hour.
Make the butter filling. Add the butter, sugar, and cinnamon to a small bowl. Combine until you have a smooth paste.
Move the dough to a floured surface and flatten it down with your hands. Try to shape it into a rectangle. Then finish flattening the dough into a 12x20 rectangle.
Spread the butter filling onto the dough. Once spread evenly, sprinkle the shredded coconut on top. Then tightly roll the dough into a cylinder. Gently with a dough scraper or knife, mark the dough in half, and each half into 6 pieces. Use a knife or unflavored dental floss to cut the dough.
Line a 9x13 baking pan with parchment paper. Place the roll with ½ inch space in between or at least equally spaced. Cover the pan with foil or plastic wrap and let the rolls rise for 1 hour or until they double in size. If making this ahead of time, *see notes*.
While the rolls rise, make the icing or frosting. In a small bowl, add the cream cheese, powdered sugar, milk, vanilla, and coconut extract. You can use a hand blender or a spoon to mix. You need to mix until everything is well combined and the frosting has no lumps. Cover and set it aside.
Preheat oven to 350°F. Uncover the rolls and bake in the middle rack of the oven for 30 minutes. Let the rolls cool before icing.
Add a tablespoon and a half of the cream cheese frosting to each cinnamon roll and enjoy. ¡Buen provecho!
Notes
Number of rolls. You can cut your rolls into whatever size you prefer. Make them smaller by cutting them thinner to about 1-inch-thick pieces. If you want larger rolls, cut them into 2 to 2 ½ inch thick pieces.
Cold proofing. If you want to make ahead, make the recipe, but don't bake it. Cover and place in the fridge overnight. Or place them in the freezer in a freezer bag. Remove from the fridge or freezer and let them get to room temperature. Then preheat your oven, and bake.
Storage. Store in an airtight container in the fridge for up to 5 days.