Coat the inside of a large (8-quart or more) non-ceramic mixing bowl with about three-quarters of the melted butter and set aside. Lay a piece of plastic wrap on a flat surface near the bowl and coat one side with remaining melted butter.
In a small mixing bowl, combine water, a pinch of sugar, and yeast. Set aside.
In a small saucepan over medium heat, combine 1 cup milk, remaining sugar, 8 tablespoons unsalted butter, honey, and salt. Stir until butter has melted and sugar dissolves. Remove from heat and let cool to lukewarm. Add yeast mixture to milk mixture and stir well to combine. Pour into the bowl of a standing mixer with a dough hook. Add eggs and mix on low speed. Add flour, about a cup at a time, stopping the mixer periodically to scrape the sides and bottom of the bowl, until the dough no longer sticks to the sides. Mix about 3 minutes longer, or turn the dough onto a lightly floured surface and knead by hand until smooth and elastic, about 10 minutes. (You don’t need extra flour if you’re using the mixer.)
Place dough into the buttered bowl and stretch the plastic wrap taut across the top, buttered side down (to keep the dough from sticking when it rises). Put the bowl in a draft-free spot at room temperature until dough doubles in volume (2 to 2-1/2 hours). Punch dough down and knead it on a lightly floured surface for about a minute. Place dough back in the bowl, cover, and let it rise until it doubles (1-1/2 to 2 hours).
Arrange the racks in your oven to accommodate two loaves of bread. Heat oven to 375°.
Line two sheet pans with parchment paper and/or cornmeal. Divide dough in half; then divide each half into three equal parts. On a lightly floured surface, roll out three of the pieces into tapered strands, each 14 to 16 inches long (midsection about 2 inches thick, end pieces about 1 inch). Arrange the strands vertically, just a fraction of an inch apart (so that you don’t stretch them too much as you braid). Starting in the middle, bring the right strand over the top of the center strand. Bring the left strand over the new center strand, and continue braiding. (Be gentle—the braid doesn’t have to be tight.) Pinch the ends together and tuck under for a smooth finish. Repeat with the top halves of the bread strands.
Place carefully on top of the sheet pan and set aside in a draft-free spot at room temperature for 20 minutes. Roll out the remaining three pieces of dough into strands and braid.
In a small bowl, combine egg yolk and milk. Brush loaves generously with mixture. Sprinkle with salt and seeds, if you’d like, and bake 30 to 40 minutes or until loaves are deeply browned and feel light and hollow when the bottom is tapped.
