In a small bowl, combine the warm water, sugar, and yeast. Stir gently and let sit for 8 to 10 minutes until foamy.
In a large bowl, whisk together the gluten free flour, tapioca starch, psyllium husk powder, and salt. Add the eggs, olive oil, and apple cider vinegar to the yeast mixture and stir to combine.
Pour the wet ingredients into the dry and mix vigorously for about 2 to 3 minutes until a thick, workable dough forms. Cover and refrigerate for 20 minutes to firm up.
Line a baking sheet with parchment paper and lightly grease it. Divide the chilled dough into 6 equal portions. With well-oiled hands, roll each piece into a smooth ball, then poke a hole through the center with your thumb and gently stretch it to about 2 inches wide.
Place the shaped bagels on the prepared baking sheet. Cover loosely with greased plastic wrap and let rise for 25 to 30 minutes until slightly puffy.
Preheat the oven to 400 F. Bring the 8 cups of water and honey to a gentle boil in a large wide pot. Carefully lower 2 to 3 bagels at a time into the boiling water. Boil for 45 seconds per side, then lift out with a slotted spoon and return to the parchment-lined baking sheet.
Whisk together the egg and water for the egg wash. Brush each boiled bagel generously with the egg wash, then sprinkle with your desired toppings.
Bake for 22 to 26 minutes, until the bagels are deep golden brown and firm on the outside. Let them cool on a wire rack for at least 15 minutes before slicing. The boiling step is what gives these bagels their signature chewy crust.