In a small bowl, stir yeast and honey into water and let mixture stand until bubbling, about 10 minutes. Stir in butter and beaten eggs.
In bowl of a standing mixer fitted with bread hook, combine flour, sea salt, and yeast-egg mixture. Mix at low speed until combined. Once dough pulls away from sides of bowl and comes together, increase speed to medium and continue to knead dough until smooth and elastic, 4–5 minutes. Add more flour, as needed, if dough is too wet or sticky. (Challah dough is traditionally a bit sticky, so resist the urge to add a lot of additional flour.) Place dough on a lightly floured surface and knead by hand for another 30 seconds, adding more flour, as needed.
Form dough into a round shape and place inside a large, buttered bowl, turning it to coat all sides. Cover bowl with a damp cloth and allow to rise in a warm place until doubled in size, about 1 hour.
Punch down dough and turn out onto a lightly floured surface. Divide dough into 3 equal size pieces, then divide each piece in half for a total of 6 pieces. Working on floured surface, roll pieces of dough into thin ropes, about 12 inches long (they should be thinner at the ends). Braid 3 of the ropes together starting at center and working out to one end, then rotate ropes and braid from the center out to the opposite end. Pinch ends together and fold them underneath. Repeat with remaining 3 dough ropes. Place braided loaves on a baking sheet lined with parchment paper and brush tops with egg wash.
Heat oven to 350°. Bake until top is a rich golden brown, 25–30 minutes. Let challah cool on a wire rack before slicing and serving.