To make the bread, place 1 cup of the water, 2 teaspoons of the sugar, and the yeast in a small bowl. Whisk to combine and let sit in a warm spot to proof for 5 minutes.
In the bowl of a stand mixer fitted with the paddle attachment, combine the flour, remaining sugar, and salt and mix on low 1 minute.
In a separate medium bowl combine remaining water, honey, oil, and eggs and whisk until smooth.
Pour yeast mixture into the bowl with the flour followed by the egg mixture. Mix with the paddle for about 30 seconds, just to combine. Switch to the dough hook and knead on medium-low for 7-10 minutes or until dough is springy and no longer sticky.
Divide dough in half and place each half in two large, oiled bowls. Roll the dough around in the bowl to coat with oil and cover with plastic wrap. Set aside in a warm place to rise until doubled in size, about 2-3 hours.
Separate each piece of dough into 3 equal pieces to make 6 pieces, divide each of those into 3 equal pieces. Roll each piece into ropes that are about a foot long and an inch wide.
Braid together 3 ropes at a time to make 6 small loaves. The author who wrote the recipe for Food 52 says, “For the nicest-looking braid, do not pinch the top edges of your logs together before braiding; simply place one log over the next and braid until you reach the bottom, then pinch those edges together. Then, flip the unfinished loaf the long way, so that the unfinished edge is now at the bottom and the loaf has been flipped over and upside down. Finish braiding and pinch these edges together. This way, both ends look identical. Tuck the very tips beneath the loaf when braiding is finished.”
Place the loaves on a floured baking sheet and refrigerate for an hour or freeze for 20-30 minutes. While loaves are chilling, prepare the water bath. Fill a high-sided, large (at least 12-inch) frying pan with water and add baking soda, whisk to combine.
Once bread has chilled, heat oven to 400°F and line two baking sheets with parchment paper. Bring the baking soda mixture to a boil over medium heat.
Once boiling, add bread, top down, one at a time and boil for 2 minutes. If it is boiling too rapidly, adjust the heat. After 2 minutes gently flip the bread over with tongs and a large spatula and boil the other side for 2 minutes. Remove to the prepared baking sheet and sprinkle the top with sea salt. Repeat with remaining loaves.
Bake loaves in, one baking sheet at a time in the middle of the oven for 15-20 minutes or until deep golden brown and baked through. Remove to a wire rack to cool for at least 15 minutes before eating.
To make the butter, combine all the ingredients in the bowl of a food processor fitted with the blade attachment and pulse to combine. Stop to scrape down the sides of the bowl frequently and keep pulsing until the mixture is smooth.