Make the dough - Add melted butter, salt, and 4¼ cups flour. Mix until a dough forms. Knead for 5–7 minutes, adding a little extra flour only if the dough is very sticky. It should be soft and slightly tacky, not dry.
3 Let it rise - Cover and let rise until doubled, about 45–60 minutes.
4 Shape the bites - Turn the dough onto a lightly floured surface. Divide into 6–8 pieces. Roll each piece into a rope about ¾ inch thick, then cut into 1-inch bites.
5 Prepare the bath - Bring 10 cups water to a boil. Add baking soda carefully; it will foam up.
6 Boil the bites - Boil the pretzel bites in batches for about 20–30 seconds. Remove with a slotted spoon and place on parchment-lined baking sheets.
7 Egg wash and salt - Brush with egg wash and sprinkle with coarse salt.
8 Bake - Bake at 425°F for 12–15 minutes, until deep golden brown.
9 Finish - Brush with melted butter if desired.