Preheat the oven to 400°F. Line a baking sheet with parchment paper.
In a small bowl, combine the warm water and maple syrup. Stir in the yeast and set it aside to proof for 5-10 minutes.
Meanwhile, combine the cassava flour, tapioca flour, and salt in a large mixing bowl. Also prepare a pot for boiling the bagels in by filling a large saucepan half full with water.
Once the yeast is puffy and bubbly, add it to the flour in the mixing bowl. Add the melted butter or oil and the eggs. Stir until a smooth batter forms. Gently stir in the blueberries. The dough should be soft but not sticky. If it seems too moist, let the dough rest for 4-5 minutes. If it seems too dry, add warm water 1 T. at a time until a soft, workable dough forms.
Bring the pot of water to a boil over medium-high heat. Divide the dough into 4 equal portions (you can also make 6 smaller bagels instead). Roll each dough portion into a ball, flatten the ball, and shape a hole in the center. Finish shaping the dough into a bagel.
Boil the bagels one at a time by dropping the bagel into the boiling water. Use a soft spatula to make sure the bagel doesn't stick to the bottom of the pot. Wait until the bagel is floating at the surface (about 1 minute), then remove the bagel and place it on the baking sheet. I find a potato masher works well for removing the bagel without scooping up the boiling water.
Once all of the bagels have been boiled, brush them with the egg wash or oil wash. Bake the bagels for 20-25 minutes or until they are golden brown.
Let the bagels cool before slicing, toasting, and enjoying!