Place warm water, 2 eggs, butter, and honey into the bowl of a stand mixer. (This recipe not recommended for hand mixing.) Add flour. Add salt to the side of the bowl and add yeast to the center of the flour.
Fit mixer with dough hook. Turn mixer to 1 and let knead 5 minutes or until dough ball forms and cleans sides of bowl.
Working on a lightly floured work surface, divide dough into fourths, then into fourths again (16 pieces). Form each piece into a ball. Using your finger, poke a hole through the center of a ball. Spin the dough ball around your finger to stretch the hole to the size you want it (note that the hole will shrink as soon as you stop). Place on a parchment lined baking sheet. Repeat with remaining dough. Let rest 15 minutes.
While dough is resting, bring 3-4 quarts of water and 2 tablespoons baking soda to a boil. Preheat oven to 375. Using a slotted spoon or spatula, slowly add each bagel to the boiling water (work in batches so as not to over crowd the pot). Bagels will sink, then float. Once floating, turn over and let boil 3 more minutes. Place bagels back onto prepared baking sheet.
Make an egg glaze by beating the yolk from the remaining egg (discard white or save for another use) with 3 tablespoons water. Brush glaze onto each bagel and top as desired.
Bake at 375 30-35 minutes.