For the dough
1/4 cup warm water (105-110 degrees)
1 envelope (2 1/4 teaspoons) active dry yeast
1 1/4 cups whole milk
2 tablespoons unsalted butter
1 egg, lightly beaten
1/4 cup sugar
1 teaspoon salt
4 cups all-purpose flour, plus more as needed

For the caramel coating
1 1/4 cups dark brown sugar
2 teaspoons ground cinnamon
1/2 cup (1 stick) unsalted butter, melted

For the bourbon crème anglaise
1 cup heavy cream
1 cup milk
6 large egg yolks
1/3 cup sugar
Pinch of kosher salt
2 tablespoons bourbon
1/2 teaspoon pure vanilla extract