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In a small saucepan over low heat, gently warm the whole milk and cubed unsalted butter until the butter melts and the mixture registers about 105°F (warm to the touch); remove from heat and let cool if needed.
In a large bowl or in the bowl of a stand mixer fitted with the dough hook, whisk together the bread flour, granulated sugar, instant yeast, and fine sea salt.
Pour in the warm milk mixture, add the egg, and mix on low speed (or stir with a wooden spoon) until a shaggy dough forms.
Turn the dough onto a lightly floured work surface and knead by hand for 8–10 minutes until smooth and elastic (or knead with the mixer for 6–8 minutes); the dough should spring back when gently pressed.
Lightly grease the bowl, place the dough inside, cover with plastic wrap or a clean kitchen towel, and let rise in a warm spot until doubled in size, about 1 to 1½ hours.
Meanwhile, in a medium bowl, stir together the softened unsalted butter, packed light brown sugar, and ground cinnamon until you have a smooth paste.
Once the dough has doubled, punch it down, turn it onto a lightly floured surface, and roll it out into a 16x12-inch rectangle.
Spread the cinnamon filling evenly over the dough, leaving a ½-inch border along one long edge.
Starting from the opposite long edge, roll the dough up tightly into a log. Slice the log into 12 equal pieces using a sharp knife or unflavored dental floss.
Grease a 9x13-inch baking dish, arrange the rolls cut side up with space between them, cover loosely, and let rise until puffy, about 30–45 minutes. Meanwhile, preheat the oven to 350°F.
Bake the rolls for 20–25 minutes, or until golden brown on top—cover with foil if they brown too quickly. Remove from the oven and let cool in the pan for 5–10 minutes.
While the rolls bake, beat together the softened cream cheese and softened unsalted butter until smooth. Gradually add the sifted confectioners' sugar, vanilla extract, and whole milk, beating until you have a pourable glaze.
Drizzle or spread the glaze over the warm rolls so it seeps into the swirls. Serve immediately, or store in an airtight container at room temperature for up to 2 days or in the refrigerator for up to 4 days.