01 - Combine warm water, granulated sugar, and active dry yeast in a large bowl. Let rest for 5 minutes until foamy.
02 - Add melted butter and fine sea salt to the yeast mixture. Gradually mix in all-purpose flour until a shaggy dough develops.
03 - Transfer dough to a lightly floured surface and knead for 5 to 7 minutes until smooth and elastic.
04 - Place dough in an oiled bowl, cover, and allow to rise in a warm location for 45 minutes, or until doubled in size.
05 - Preheat oven to 450°F. Line two baking sheets with parchment paper and lightly oil the surfaces.
06 - In a large pot, bring 10 cups water and baking soda to a vigorous boil.
07 - Punch down risen dough and divide into 4 equal portions. Roll each into a 12-inch rope, then cut into 1-inch pieces.
08 - Working in batches, carefully add pretzel bites to the boiling baking soda solution for 30 seconds. Remove with a slotted spoon and arrange on prepared baking sheets.
09 - Whisk egg yolk with 1 tablespoon water to create an egg wash. Brush pretzel bites and sprinkle with coarse sea salt.
10 - Bake in preheated oven for 12 to 14 minutes until the pretzel bites are deep golden brown. Let cool slightly before serving.
11 - In a small bowl, blend softened butter, white miso paste, honey, and lemon juice until smooth and uniform.
12 - Offer warm pretzel bites with miso butter for dipping or spreading.