In a large bowl mix your flour, and cut butter into flour with a pastry cutter or using the tips of your fingers, crumble into pea size. Alternatively you can use a mixing stand with the paddle attachment and mix on a medium speed until the butter is pea size. In a separate medium bowl, whisk sourdough starter, maple syrup, nut milk, carrot juice (I use my own juicer and sub the pulp for the grated carrots!), turmeric powder, and grated carrots (if using store bought juice). Add the wet ingredients to the flour and butter mixture and mix with your hands in a claw-like hand-position. You can again use your paddle attachment and mixer, or a spoon. Mix until all the dry ingredients are completely incorporated, but not over-mixing or kneading like you would bread. We do not want to build lots of strength, otherwise you will have a more chewy cinnamon bun! Let this dough sit out in room temperature, covered with cellophane or a plastic bag, for about 8-10 hours (I like doing this over night).
Once dough has fermented, sprinkle the baking powder, baking soda, and salt onto the dough, and knead the ingredients in by folding the dough over on itself and keep mixing. While the dough sits for 20 minutes to rest, prepare sticky glaze by cutting the vegan butter into small cubes (1cmx1cm), and sprinkle evenly in a spring form cake pan (9in), casserole dish (~8x8), or cast iron. Use baking parchment if you know your pan tends to stick! Sprinkle the coconut sugar or brown sugar in an even layer on the bottom of the baking dish on top of the butter, then top with chopped pecans and set aside.
On a lightly floured surface, roll out the dough into a thin rectangle (8inx20in). Brush with 1/4 cup melted coconut oil and top with 1/2 cup brown sugar (or granulated sugar), cinnamon, and ginger.
Starting at one end, tightly roll up the dough and situate seam side down. Then with a bench scrapper or chef knife, cut the dough into 1.5 - 2 inch sections and position in your baking dish with the glaze layer on the bottom (you should have about 10 - 12 rolls). Cover with a damp towel and set on top of the oven to let it briefly rise again while you preheat oven to 400F.
Once the oven is hot, bake rolls for 25-30 minutes or until golden brown. Let cool for a 5 minutes, then carefully invert onto a big plate and serve immediately.