In a large mixing bowl, combine the warm water, honey, and active dry yeast. Stir gently and let it sit for 5-7 minutes until the mixture is foamy.
Add the gluten-free sourdough discard to the yeast mixture and stir to combine.
In a separate bowl, whisk together the gluten-free all-purpose flour blend, brown rice flour, tapioca starch, and salt.
Add the dry ingredients to the wet ingredients in the large mixing bowl.
Add the eggs, olive oil, and apple cider vinegar to the mixture.
Using a stand mixer fitted with a paddle attachment or a hand mixer, mix on medium speed for 3-4 minutes until the dough is smooth and sticky. The dough will be more like a thick batter than traditional bread dough.
Lightly grease a 9×5-inch loaf pan with oil or nonstick spray.
Pour the dough into the prepared loaf pan and smooth the top with a wet spatula.
Cover the pan loosely with plastic wrap or a clean kitchen towel and let the dough rise in a warm place for 45-60 minutes, or until it has risen to about 1 inch above the rim of the pan.
Preheat the oven to 375°F (190°C).
Remove the cover and place the loaf pan in the preheated oven.
Bake for 45-50 minutes until the top is golden brown and a toothpick inserted into the center comes out clean.
Remove the bread from the oven and let it cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing.