Place the warm water and coconut sugar into the bowl of a stand mixer, and stir to dissolve. Sprinkle with yeast; let stand for 5 minutes, or until foamy. Using the dough hook attachment, beat 1 cup of flour into the yeast mixture at low speed until combined. Add 4 more cups of flour; mix until combined, about 30 seconds. Raise speed to medium-low; continue beating until dough pulls away from the sides of the bowl, about 1½ minutes. Add ½ cup flour; knead on low speed 1 minute more. If the dough is still wet and sticky, add ½ cup more flour; knead until combined, about 30 seconds.

Turn out the dough onto a lightly oiled and floured work surface, and knead until smooth, about 10 times. I also oil my hands to keep them from getting covered in the sticky gluten-free dough! Transfer the dough to a lightly oiled bowl. Cover with a kitchen towel, and let rise in a warm place until the dough has doubled in bulk, about 1 hour. Preheat the oven to 450ºF. Lightly coat two baking sheets with cooking spray; set aside. Punch down the dough to remove air pockets. Turn out onto a lightly oiled and floured work surface. Oil your hands if needed to prevent sticking. Knead once or twice and divide into 16 equal pieces (use a dough cutter to help make even divisions). Cover the dough with plastic wrap.

Meanwhile, fill a large shallow pan with 2 inches of water, and bring to a boil. I like to use two of my widest, shallow pans so I can cook two per pan at a time and do four at a time. Add baking soda to each pan. Reduce to a simmer, and carefully drop two pretzels per pan into the water. Poach for 1 minute. I use two kitchen timers, one for one pan and one for the other. Use a slotted spoon to return the pretzels to the baking sheet. Continue until all pretzels are poached.

Brush pretzels with the whisked eggs or melted butter and sprinkle with coarse salt. Bake pretzels until golden brown, 12-15 minutes.

Remove from the oven and let cool on a wire rack. Pretzels will keep at room temperature for up to 2 days. Do not store them in a covered container. Serve warm or at room temperature. This is a great make-ahead recipe. Simply cook and cool completely, store in the freezer in a 9 x 13-inch pan layered with greased parchment paper or a large Ziploc bag layered with greased parchment paper. I prefer flash-freezing the pretzels on greased parchment paper so they lie flat, then transferring them to containers. Thaw the night before, and warm them up (covered) before serving.