In a large bowl, whisk together the warm milk, instant yeast, and granulated sugar. Let sit 5 minutes until slightly foamy.
Add the eggs, 1/4 cup very soft butter, and a small amount of pink gel food coloring (or beet puree). Whisk until mostly smooth.
In a separate bowl, combine 3 cups flour and 1/2 teaspoon salt. Add this to the wet ingredients and stir with a wooden spoon or dough hook until a shaggy dough forms.
Knead the dough by hand on a lightly floured surface or with a stand mixer on medium-low speed for 6–8 minutes, adding a spoonful of flour at a time only if very sticky, until smooth, elastic, and slightly tacky. Adjust the pink color by kneading in a tiny bit more gel if needed.
Shape the dough into a ball, place it in a lightly greased bowl, cover, and let rise in a warm place until doubled in size, about 60–75 minutes.
While the dough rises, make the filling by stirring together 1/3 cup very soft butter, brown sugar, cinnamon, cardamom or nutmeg (if using), and a pinch of salt until you have a thick, spreadable paste.
Lightly grease a 9x13-inch baking pan. Once the dough has doubled, gently punch it down and turn it out onto a lightly floured surface.
Roll the dough into a rectangle about 12x16 inches, with the long side facing you. Spread the cinnamon filling evenly over the surface, leaving a 1/2-inch border on the long edge farthest from you.
Starting from the long edge closest to you, roll the dough up tightly into a log, pinching the seam to seal.
Trim the ends if uneven, then cut the log into 12 equal pieces using a sharp knife or dental floss.
Arrange the rolls cut-side up in the prepared pan, leaving a little space between each roll. Cover loosely and let rise until puffy and nearly touching, about 30–40 minutes. For an overnight option, cover and refrigerate up to 12 hours, then let sit at room temperature 30–45 minutes before baking.
Near the end of the second rise, preheat the oven to 350°F. Bake the rolls for 22–25 minutes, until the tops are lightly golden and the centers look set but still soft.
While the rolls bake, make the glaze by whisking together powdered sugar, milk or cream, vanilla, and a pinch of salt until smooth. For a tangier glaze, whisk in the soft cream cheese until fully blended and pourable.
Let the rolls cool in the pan for 10–15 minutes, then spoon or drizzle the sweet vanilla glaze over the warm rolls, letting it seep into the spirals. Serve warm.