Combine 2 cups flour, yeast, sugar, and salt. In another bowl, whisk milk, melted butter, and egg. Mix into dry ingredients. Knead in remaining flour until smooth, about 8 minutes. Cover and let rise until doubled, 1 hour.

While dough rises, whisk brown sugar, butter, cream, and salt in a saucepan over medium heat until melted and smooth, about 3 minutes. Pour into a 9x13-inch baking dish.

Punch down dough. Roll into a 16x12-inch rectangle. Spread softened butter, then sprinkle with brown sugar and cinnamon. Roll up tightly from the long side, seal seam.

Cut into 12 slices. Arrange cut side down in the caramel-lined pan. Cover and let rise until puffy, 30 minutes.

Preheat oven to 350°F (175°C). Bake until golden, 25-30 minutes. Cool 5 minutes, then invert onto a platter, scraping any caramel from the pan.