Pour the lukewarm milk into a bowl and sprinkle the yeast and 3 1/2 tablespoons sugar over it. Let this mixture sit undisturbed for 5 minutes—this bloom time activates the yeast and ensures proper fermentation. Add the softened 3 tablespoons butter, then mix in 2 cups of flour and the salt, mixing for about 2 minutes until combined. Add the remaining 1 1/4 cups flour and mix until a soft, shaggy dough forms. Knead the dough for 5 minutes until it becomes smooth and slightly elastic.
Place the dough from Step 1 in a lightly greased bowl, cover with a damp towel or plastic wrap, and let it rise at room temperature for 2 hours until roughly doubled in size. After rising, flatten the dough into a 10x14 inch rectangle on a lightly floured surface, cover it, and chill in the refrigerator for 20 minutes. This chilling step makes the dough easier to work with and prepares it for the lamination process.
While the dough chills, mix the 1 1/4 cups cold butter with 1 tablespoon flour in a bowl until it forms a spreadable paste—this prevents the butter from tearing through the dough. Remove the chilled dough from the fridge and spread the butter mixture over the center two-thirds of the rectangle, then fold the dough into thirds like a letter (folding the unbuttered third first, then the other side over top) and seal the edges gently. Roll the folded dough into a 9x12 inch rectangle and fold into thirds again, then chill for 20 minutes. Repeat this rolling-and-folding process two more times (for a total of three folds), chilling for 20 minutes between each fold. I find that these multiple folds create the beautiful, flaky croissant layers that make these muffins special—patience with the chilling steps really pays off in the final texture.
While the final laminated dough chills, preheat your oven to 350°F and grease a 12-cup muffin pan. In a small bowl, mix together the 3/4 cup sugar, 1 1/2 tablespoons cinnamon, and 1/4 teaspoon ground nutmeg—this is your cinnamon-sugar filling and topping.
Remove the laminated dough from the fridge and cut it into 3 equal pieces. Working with one piece at a time, roll it into an 8x12 inch rectangle and sprinkle 2 tablespoons of the cinnamon-sugar mixture over the entire surface. Cut the rectangle into 12 thin strips (about 2/3 inch wide), stack 3 strips on top of each other, then roll the stack into a tight spiral. Place each spiral seam-side down into a muffin cup. Repeat with the remaining two pieces of dough and cinnamon sugar. I like to add about 1/2 tablespoon of Nutella to the center of each spiral before rolling for extra richness, but this is optional—it creates a delicious surprise when you bite into the warm muffin.
Cover the muffin pan with a damp towel or plastic wrap and let the shaped muffins rise at room temperature for 1 hour until they're puffy and nearly doubled. Bake in the preheated 350°F oven for 25 to 28 minutes until the muffins are golden brown and register an internal temperature of 200°F when a thermometer is inserted into the center of one.
Remove the muffins from the oven and let them cool in the pan for 2-3 minutes until they're still warm but handleable. Turn them out onto a plate or work surface while still warm and roll them in the remaining cinnamon-sugar mixture to coat all sides. Serve warm for the best croissant-like texture and flakiness.