Bloom the yeast: In a large bowl, whisk the warm milk with the granulated sugar and yeast, then let stand until foamy, 5–10 minutes.
Make the dough: Whisk in the egg, then add the softened 4 tbsp butter and salt; mix until combined, 1 minute. Add half the flour and mix until shaggy, 1–2 minutes. Add the remaining flour and knead by hand or mixer until smooth, elastic, and slightly tacky, 8–10 minutes.
First rise: Lightly grease a clean bowl with a thin film of neutral oil. Place the dough in the bowl, turn to coat, cover, and let rise in a warm spot until doubled in size, 60–75 minutes.
Prepare the filling: In a small bowl, stir together the brown sugar and ground cinnamon until evenly combined, 30 seconds.
Prepare to shape: Lightly oil your work surface and a 9×5-inch loaf pan with the remaining neutral oil (about 1 tbsp total), 30 seconds.
Roll out: Gently deflate the dough and roll it into an 8×18-inch rectangle, about 0.25 inch thick, 2–3 minutes.
Fill: Spread the softened 3 tbsp butter evenly over the dough, leaving a 0.5-inch border on all sides, 1–2 minutes. Sprinkle the cinnamon-sugar mixture evenly over the butter and press lightly to adhere, 30–60 seconds.
Form the loaf: Starting from a short 8-inch side, roll the dough up tightly into a log, 1–2 minutes. Pinch the seam and ends to seal, then tuck the ends under, 30 seconds.
Pan and proof: Place the log seam-side down in the prepared loaf pan, cover, and let rise until the dough crowns about 1 inch above the rim and springs back slowly when gently pressed, 45–60 minutes.
Bake: Preheat the oven to 350°F during the final 20 minutes of proofing. Bake the loaf until deep golden brown and the center reaches 190°F, 35–45 minutes; tent with foil after 20 minutes if browning too quickly.
Cool: Let the bread cool in the pan for 15 minutes, then turn out onto a wire rack and cool completely before slicing, at least 1 hour.