Into the bowl of stand mixer, pour 2 cups of flour, yeast, 1/2 cup grated carrot + orange zest. Use a fork or whisk to evenly disperse the ingredients throughout the flour.
In a small saucepan over medium heat, warm milk, sugar, 1/3 cup of butter, and salt until it reaches 120-130 degrees. Add this to the bowl of flour. Using the dough hook attachment, mix it on low speed for 15-20 seconds.
Add the 2 eggs. Beat on low for 30 seconds, scrape down the sides and beat on medium for about 3 minutes.
Add the remaining 2 cups of flour, 1 cup at time. Beat just until each cup is incorporated and scrape down the sides in between. The dough may still appear sticky and a little on the wet side. The carrots have released some juices into the dough.
Dust a work surface with the remaining 2 Tbsp of flour and turn your dough out. Sprinkle a little more flour on your hands. Knead by hand for 3 to 5 minutes, incorporating all the flour.
Shape it into a ball and place it in a lightly greased bowl. Turn it over once to coat, cover and set in a warm, dry spot for about 1 hour. It will double in size. (I like to proof mine in the oven with just the oven light on.)
Meanwhile, make the spice filling by combining brown sugar, honey, cinnamon, clove, nutmeg and ginger in a small bowl. Add the remaining 1 cup of grated carrot and pecan pieces and stir.
Punch down the dough. Dust your work surface and roll the dough into a large rectangle about 14" x 16".
Spread the filling all over the dough, nearly to the edges. Starting on the longer side, roll the dough then cut into 16 equal rolls.
Place the giant rolls into a 9"x13" cake pan, lightly greased. Cover them and allow to rest for another 30-45 minutes. They will expand to fill the pan.
Preheat the oven to 350 degrees. After the rolls have rested, bake them for 20 minutes. Check them for doneness. The dough around the edges of the pan may turn a very light golden brown. If they are still pale, bake them for up to 5 minutes longer. Remove them to cooling racks.
Prepare the icing by combining what's left of the stick of butter with the cream cheese. Beat them with a hand mixer or with a whisk until it is smooth. Add 1/2 cup of confectioner's sugar and mix carefully. Add the vanilla, 2 Tbsp of orange juice and remaining cup of confectioner's sugar and mix. Add 1 to 2 more Tbsp of orange juice until the icing reaches your desired consistency. Mix until smooth.
Drizzle icing over the rolls and use an offset spatula or back of a spoon to spread.