1/2 cup unsalted butter, softened to room temperature
5 tbsp brown sugar
3 cups confectioners sugar
1 tsp vanilla. extract
1/8 tsp salt
Directions
In a small, heatproof bowl, microwave 1/3 cup. milk and 1 tbsp brown sugar (when removed from the microwave, temp should register 110 degrees), stir to dissolve sugar. Sprinkle yeast over, stir to combine and let sit 5 minutes.
In another small heatproof bowl, whisk 1/4 cup flour and remaining 1/2 cup milk until smooth. Microwave in 15-second increments, whisking between each, until warmed through and smooth. About 1 minute total.
In the large bowl of a stand mixer fitted with the dough hook, combine yeast mixture and flour mixture. Add eggs, butter, orange zest, salt, vanilla and remaining 3 cups flour and 2 tbsp brown sugar. Beat on medium-low speed until a dough forms, 10-12 minutes. Spray a large bowl with cooking spray and place. dough in bowl. Cover with plastic wrap and let rise in a warm place until dough is doubled in size, about 1 hour.
In a small bowl, stir butter, cinnamon, cardamom, and 5 tbsp brown sugar until smooth.
Place a 20" piece of parchment paper on your work surface; lightly dust with flour. Gently punch dough down and turn out onto parchment. Dust rolling pin with flour and gently roll dough to an 18" by 10" rectangle. Spread brown sugar butter over dough. Spread Satsuma jelly over butter. Slide parchment with dough onto a sheet pan and refrigerate until cold, about 15 minutes.
With long side of dough facing you, lightly roll dough away from you creating a spiral, ending seam side down. Using a serrated knife, cut dough into 12 rolls. Arrange dough in a 12" cast iron skillet. Cover skillet with plastic wrap. Place in a warm area to rise until almost double in size, about 1 hour.
Preheat oven to 350 degrees. Remove plastic wrap. In a small bowl, whisk egg and a splash of water until combined. Pour cream over dough; brush with egg wash.
Bake rolls until tops are golden brown and cream is absorbed, 28-32 minutes. Let cool 10 minutes.
Mix together glaze ingredients and spread over the top of the rolls.