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Step 1
Combine the warm water and instant yeast in the bowl of a stand mixer. Let sit for 15 minutes. Meanwhile, add the butter to a small saucepan over medium heat and allow to melt. Turn the heat to low and continue to cook until the butter is browned and fragrant. Let cool slightly.
Step 2
While the butter browns, add the milk and cinnamon sticks to another small saucepan over low heat. Let steep for 10 minutes. Remove the cinnamon sticks.
Step 3
Add the sugar and eggs to the bowl with the yeast. Whisk to combine. Whisk in the browned butter, steeped milk, and vanilla extract. Pour in the sifted flour and salt. Using a dough hook, mix on medium-low speed for 5 minutes until the dough is smooth and starts to pull away from the sides of the bowl.
Step 4
Turn the dough out onto a floured surface. Form it into a ball. Place it into a lightly floured bowl and cover with plastic wrap. Allow to rise in a warm place (a 100°F oven or by the fire are ideal spots) for 1 hour until doubled in size. Punch the dough down and dump it back onto a floured surface. Roll into a 12×18” rectangle.
Step 5
For the filling, mix the butter, brown sugar, cinnamon, and salt together in a bowl. Spread it onto the dough in an even layer. Roll the dough lengthwise into a log. Use a sharp knife to cut the dough into 12 even pieces. Place the pieces, filling-side up, into a 9×13” baking dish. Wrap and chill overnight.
Step 6
In the morning, let the rolls sit in a warm place for another hour (they should rise a bit). Combine the egg yolk and milk. Brush this onto the rolls and sprinkle with the raw sugar.
Step 7
Bake at 350°F for 30 minutes, or until golden brown. Serve warm with the mascarpone icing (recipe below) drizzled over top.
Step 8
Combine the mascarpone, powdered sugar, water, and vanilla in a mixing bowl.
Step 9
Whisk well until smooth.
Step 10
Serve at room temperature.