In a small bowl, mix together ¼ cup warm water and 1 teaspoon sugar. The temperature of the water should be between 100° and 110° Fahrenheit. Add in the entire packet of active dry yeast. Mix gently and then let it sit for about 10 minutes until it starts to bubble and rise.*If the yeast does not bubble and rise, then that means the yeast is bad and you'll need to start over. You cannot use expired or bad yeast because then the bagels won't rise properly. Also, if the water is too hot that can kill the yeast so use a thermometer to get an accurate temperature.
While the yeast is activating, add 1 ¼ cups warm water, 2 tablespoons brown sugar, and 1 tablespoon Kosher salt to a mixing bowl on a stand mixer.
After the yeast has activated for about 10 minutes, add it to the liquid in the mixing bowl.
Add in 2 cups of the gluten-free flour blend and mix with the paddle attachment until it's well incorporated. Add in the remaining 2 cups of gluten-free flour. The final dough is smooth and slightly tacky, but not sticky.
Lightly flour (with gluten-free flour, of course) a marble surface or parchment paper on the counter and scrape all of the dough out of the mixing bowl onto the surface. Sprinkle the top of the dough with a little more gluten-free flour.
Divide the dough into 8 equal portions. If you are using a kitchen scale, then you are looking for a weight of approximately 115 grams each, but it's OK if they are not exactly the same size.
Roll the dough into round balls. Place the dough balls on a baking sheet lined with parchment paper and lightly sprinkled with gluten-free flour. Poke your finger in the middle of each ball and make a hole about 1-1½ inches wide. Cover the baking sheet in plastic wrap and place in the refrigerator overnight (at least 8 hours).
Remove the formed bagel dough from the refrigerator and let it come to room temperature. While waiting for the dough to warm up, preheat the oven to 400° Fahrenheit.
In a large pot on the stovetop, heat 6 cups of water, 2 tablespoons of brown sugar, and 1 tablespoon of baking soda until it comes to a rolling boil. Add in the bagels (about 2 at a time) and boil for 30-45 seconds, flipping halfway through.
Line another baking sheet with parchment paper and sprinkle with the corn meal. Use a wire scoop to remove the bagels from the water. Let the water drip off and place the drained bagles on the baking sheet right on top of the corn meal. *The bagels will expand after the water bath, so you might need to use 2 baking sheets for the baking part.
Make an egg wash by whisking the egg and 1 tablespoon water. Brush the boiled bagels with the egg wash and then bake in a 400° oven for 20 minutes until they are golden brown.