In a large mixing bowl, combine the all-purpose flour, granulated sugar, instant yeast, and salt. Whisk together until well combined.
Add the chilled butter slices to the flour mixture. Using a pastry cutter or your fingers, cut the butter into the flour until it resembles coarse crumbs with some pea-sized pieces remaining.
In a separate bowl, whisk together the sour cream, orange juice, and ice water. Gradually add this mixture to the flour and butter mixture. Stir until just combined; it’s okay if there are some lumps.
Turn the dough out onto a lightly floured surface. Knead gently for about 1 minute until it comes together. Wrap the dough in plastic wrap and refrigerate for at least 1 hour.
In a medium bowl, combine the granulated sugar, light brown sugar, grated orange zest, ground cinnamon, and vanilla extract. Mix well to create a fragrant filling.
After the dough has chilled, remove it from the refrigerator and turn it out onto a floured surface. Roll it into a rectangle about ¼ inch thick.
Sprinkle the filling evenly over the rolled-out dough, leaving a small border around the edges.
Starting from one long side, tightly roll the dough into a log. Once rolled, slice the log into 12 equal pieces.
Place the sliced buns cut side up on a baking sheet lined with parchment paper. Cover with plastic wrap and let them rise in a warm place for about 30 minutes.
Preheat your oven to 375°F (190°C) while the buns are rising.
In a small bowl, whisk the egg yolk with a tablespoon of water. Brush this mixture over the tops of the buns for a beautiful golden finish.
Bake the buns in the preheated oven for 25-30 minutes, or until they are golden brown and cooked through.
Remove the buns from the oven and let them cool slightly on a wire rack before serving. Enjoy them warm, perhaps with a drizzle of icing or a dusting of powdered sugar.
