1. In the bowl of a stand mixer, mix together water, sugar, and yeast. Let stand for five minutes.
2. In a separate bowl, combine the flour and salt.
3. To the yeast mixture, add the egg, honey, and half the flour-salt mixture on low speed with a paddle attachment until well combined. Add the remainder of the flour-salt mixture, and combine.You should have a dough that's just lightly sticky, and not dry. If you can't roll or mold it, you may need more flour.
4. On a very lightly floured work table, divide the dough into five equal pieces.
5. Very carefully and lightly roll the dough into 6 inch long ropes, then twist into a pretzel shape. Using a spatula, carefully transfer to a parchment lined baking tray.
6. Brush each pretzel heavily with rice bran oil or melted allergy-friendly butter. Cover the tray lightly with a damp cloth and place in a warm spot (70 - 75 degrees F) to rest and proof for 30 minutes.
7. While the dough is proofing, preheat your oven to 375° F.
8. In a pot on the stovetop, bring 5 cups of water to a boil, then add the baking soda. Stir to ensure the baking soda is dissolved completely.
9. When the soda bath is boiling, gently place the pretzels in the bath. Boil for 25 seconds. Flip them and boil for another 10 seconds. Remove from the pot using a slotted spoon or spatula, and drain as much water as you can. Place on a parchment lined baking tray.
10. Brush each pretzel heavily with the melted butter replacer, and sprinkle with coarse salt. Bake in the oven for 10 - 12 minutes until golden brown.
11. Serve pretzels warm out of the oven. If you prefer to save them for another time, cool completely, wrap tightly, and freeze.