Make the dough first. In a large mixing bowl, or the bowl of a stand mixer. Add the warm apple cider, it should be around 100 degrees, which is warm to the touch but shouldn't burn your finger.
Then sprinkle in the yeast. Let the yeast bloom and bubble for about 5 minutes. It should get nice and bubbly.
Now, add the brown sugar, salt and coconut oil.
Next, if you are using a stand mixer, put the bowl onto the stand and attach the dough hook. Then start adding the flour, about a cup at a time. About 3 and 3/4 cup should be perfect, but add about 1/4 a cup more if needed until the dough isn't sticky anymore. Using the dough hook to mix and knead.
Add the cinnamon to the dough and then let it knead with the dough hook for about 3 minutes.
Let the dough rest and rise for about 10 minutes. It should puff up a bit.
Now, turn the dough out onto a floured surface and cut into about 8 equal pieces.
Then roll each piece out into a long rope with the palms of your hands. It should be about 20 inches long.
Now, form a U-shape, then holding the ends of the rope, cross them over and under each other and press the ends onto the bottom of the pretzel.
Next, in a large pot, add the 9 cups of water and the baking soda and heat on medium high. Stir and bring to a boil. reduce heat to medium, so it is not at a heavy boil.
Carefully adding 1-2 pretzels at a time, boil for 30-60 seconds. Then place on a baking sheet with a silicone mat or parchment paper lining it. Repeat with all of the pretzels.
Preheat the oven to 400 degrees(F).
Bake the pretzels for 12-15 minutes or until golden brown.
While the pretzels bake, make the coating and the icing.
First, mix the sugar and cinnamon for the coating together in a large mixing bowl. Set aside.
Next, if you are making the icing, add the powdered sugar to a medium sized mixing bowl and then add the maple syrup,1 tablespoon apple cider and pinch of salt, if it needs to be thinner, add another tablespoon of apple cider. Set aside.
Once the pretzels are done, remove them from the oven and brush each of them with the melted vegan butter. Place them in the bowl with the sugar and cinnamon and coat completely.
Serve warm with the icing. They reheat well!