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Step 1
Make the dough first by pouring 1/2 cup of the carrot juice in a small pot and heating it on high for 10 to 15 seconds until the chill of the carrot juice has been taken off and it is at roughly room temperature or a slightly warmer (don’t bring it to a boil). Sprinkle the yeast over the warm juice.
Step 2
Stir the yeast into the juice to dissolve. Set aside for about 5 minutes or until it starts to bubble.
Step 3
While the yeast proofs, place the flour, both sugars, salt and pumpkin pie spice blend into the bowl of a food processor. Pulse until the dry ingredients are uniform in color.
Step 4
Cut up 1/4 cup (57 g or 1/2 stick) of butter into 1/2-inch chunks and add to the food processor bowl. Pulse in 1-second increments until the butter is mostly broken up into pebble size bits (it’s ok if a few pieces are bigger).
Step 5
Cut the remaining butter into 1/2-inch chunks and add to the bowl. Pulse twice in 1-second increments. The butter will still be chunky; that’s ok.
Step 6
Once the yeast is bubbly add the remaining carrot juice to the pot and stir together (if the liquid isn’t bubbly, dump it and start over with fresh yeast and new carrot juice). Pour the yeasty juice into the food processor bowl, then pulse an additional 3 times in 1-second increments. Again the butter will still be chunky.
Step 7
A dough won’t form yet, so don’t worry. Empty the entire content on a clean surface and remove the processor blade carefully.
Step 8
Gather all the ingredients together with your hand and start to fold, massage and knead it together until a ball forms. You should only have to do this a few times.
Step 9
Push the dough into a rough rectangle and then sprinkle some flour under the dough and on top of it. Roll the dough out to a 12 x 15 rectangle so the long side is facing you (it should be “landscape” orientation).
Step 10
Fold the top 1/3 of the dough down.
Step 11
Then fold the bottom 1/3 of the dough up over that fold, creating a long and skinny 4 x 15 inch rectangle.
Step 12
From the short end, roll the dough up as if you were forming a giant cinnamon bun.
Step 13
You’ll end up with a tall skinny roll with the spiral facing you.
Step 14
Flatten the roll down from the top with the palm of your hand until the dough is roughly 1 1/2 to 2 inches thick. Place in a gallon zip-top plastic bag and let rise at room temperature for 1 hour. Move the bag with the dough in it to the refrigerator and let chill for at least 1 hour or up to overnight
Step 15
To assemble, brush about 1/2 of the melted butter in the cups of a standard 12 muffin tin. Generously dust the inside of the muffin cups with sugar, about 1 teaspoon per cup, using about 2 tablespoons of sugar total. Place the tin on a rimmed baking sheet.
Step 16
Combine the remaining sugar, brown sugar, orange zest, pumpkin pie spice blend and salt in a bowl with a fork.
Step 17
Once the dough has chilled, take it out of the bag and place it on a clean floured surface. Roll the dough out into a 15 x 21 inch rectangle, with the long side is facing you (again it should be “landscape” orientation). Try to make the corners as “square” as possible.
Step 18
Fold the left edge of the dough 1/3 of the way toward the center.
Step 19
Then fold the right edge over the first fold.
Step 20
You're forming a 7 x 15 inch rectangle with three layers. Turn 90 degrees and roll out until you have an 8 x 18 inch rectangle.
Step 21
Brush the top of the dough with the reserve melted butter.
Step 22
Sprinkle the filling over the dough evenly.
Step 23
Tightly roll the dough up from the bottom edge form a long and skinny 18-inch long roll.
Step 24
Slice the dough into 1 1/2-inch pieces.
Step 25
Place each bun into the prepared muffin tin swirl side up. Cover loosely with plastic wrap and let rise for 1 hour at room temperature.
Step 26
About 15 minutes before the buns have finished rising, preheat the oven to 375ºF. Once the buns have risen (they won’t have risen much, just about 1 1/2 times and look a little more puffy), remove the plastic wrap and bake in the oven until they are golden brown on top, about 35 to 40 minutes.
Step 27
Once the buns are out of the oven, immediately remove them from the pan with two forks to a wire cooling rack. Don’t touch them with your fingers (they’ll be really hot!) but don’t wait for them to cool, as the sugar will harden and it will be impossible to remove them. Let cool on the rack for a minute or two and then finish them by pour 1/2 cup of granulated sugar into a large heatproof bowl and adding a bun to the sugar. Roll it around the sugar to coat it and then move it back to the wire rack. Repeat with the remaining buns, adding more sugar if needed. Serve immediately.