Bloom the yeast. In a large bowl, combine warm milk and 1 tablespoon of the granulated sugar. Sprinkle the yeast over the top and let it sit for 5–10 minutes until foamy. If it doesn’t foam, your yeast may be expired or the milk too hot or cold.

Mix the dough. Add the remaining granulated sugar, softened butter, egg, vanilla, and salt to the yeast mixture. Stir to combine. Add 3 1/2 cups of flour, one cup at a time, mixing until a shaggy dough forms.

Knead until smooth. Turn the dough onto a lightly floured surface. Knead for 8–10 minutes, adding small sprinkles of flour only as needed, until the dough is smooth, soft, and slightly tacky but not sticky. Aim for a dough that springs back when pressed.

First rise. Place the dough in a lightly oiled bowl, turning to coat. Cover with a towel or plastic wrap and let rise in a warm, draft-free spot for 60–90 minutes, or until doubled in size.

Prep the filling. In a small bowl, mix the cinnamon, granulated sugar, and brown sugar. Melt the 3 tablespoons of butter and set aside. Grease a 9x5-inch loaf pan and line the long side with a parchment sling for easy removal.

Roll it out. Punch down the dough and roll it into a 9x16-inch rectangle on a lightly floured surface. Brush the surface with melted butter, leaving a 1/2-inch border on one short side.

Add the swirl. Sprinkle the cinnamon-sugar mixture evenly over the buttered dough. Gently press it in with your hands to help it stick.

Shape the loaf. Starting from the short side opposite the clean border, roll the dough into a tight log. Pinch the seam to seal and tuck the ends slightly under. Place seam-side down in the prepared pan.

Second rise. Cover the pan and let the dough rise again for 35–50 minutes, or until it crowns about 1 inch above the rim. Preheat the oven to 350°F (175°C) during this rise.

Bake. Bake for 30–38 minutes, until the top is deep golden and the center registers around 190–195°F on an instant-read thermometer. If the top browns too quickly, tent loosely with foil for the last 10 minutes.

Cool and glaze. Let the loaf cool in the pan for 10 minutes, then lift it out to a rack. Whisk powdered sugar, vanilla, and 2 tablespoons of milk or cream until smooth and pourable. Add more liquid if needed. While the bread is warm, drizzle the glaze over the top, letting it drip down the sides.

Slice and serve. Cool at least 30 minutes before slicing so the swirl sets. Serve slightly warm for the best texture and aroma.