In the bowl of a stand mixer fitted with a dough hook, whisk together the water, milk, yeast, and 2 tablespoons of sugar. Loosely cover and let it sit for 5-10 minutes, until foamy and frothy on top.
½ cup water, ½ cup whole milk, 2 ¼ teaspoons instant or active dry yeast, ¼ cup sugar
Add the remaining sugar, butter, 1 cup of flour, and salt. Beat on low speed for 30 seconds, scrape down the sides with a silicone spatula, then add another cup of flour. Beat on medium speed until relatively combined (there may still be chunks of butter). Add the remaining flour and continue beating on medium speed until the dough comes together and pulls away from the sides of the bowl, about 2 minutes.
4 tablespoons unsalted butter, 3 cups bread flour, 1 teaspoon salt
Keep the dough in the mixer and knead for an additional 8-10 minutes.
Lightly grease a large bowl with oil or nonstick spray. Place the dough in the bowl, turning to coat all sides. Cover and let it rise in a warm place for 1-2 hours, or until it doubles in size.
Grease a 9x5-inch loaf pan or cover with parchment paper.
Prepare the swirl in a small bowl, and whisk together the sugar and cinnamon.
When the dough is ready, punch it down to release the air. Lightly flour a work surface, your hands, and a rolling pin. Roll the dough into an 8x20-inch rectangle. Brush the surface with beaten egg white and sprinkle with the cinnamon-sugar mixture. Roll the dough into an 8-inch log. Place the log seam-side down into the prepared loaf pan.
1 egg white, ¼ cup sugar, 2 teaspoons ground cinnamon
Cover the loaf and allow it to rise for 1 hour, or until it’s about 1 inch above the top of the loaf pan.
Preheat the oven to 350°F (180°C), adjusting the rack to a lower position. Once the dough has risen, melt the remaining tablespoon of butter and lightly brush it over the top of the loaf. Bake for 35-45 minutes, or until golden brown. Check halfway through—if the top is browning too quickly, tent with aluminum foil.
1 tablespoon unsalted butter
Remove the bread from the oven and let it cool for a few minutes in the pan on a cooling rack. Remove the loaf from the pan and cool it on the rack for at least 10 minutes before slicing.
Serve warm and enjoy!