Preheat oven to 475˚ and line a large baking sheet or two with parchment paper.
Combine starter with the water and mix well till smooth. Stir in salt and 1 Tbs of melted butter. Add 1 cup of flour at a time and knead on lowest setting until dough forms and is no longer very sticky. You may need more or less depending on the temperature difference. Knead dough for 5 minutes or until smooth and pliable.
Form a dough into a ball by hand. Lightly grease a bowl and let dough rest for 15 minutes. Cover with a damp towel.
In a medium sized pot, boil 2 cups of water with 2 Tbs of baking soda. Once the baking soda is mostly dissolved, take the mixture off of the heat and pour into a shallow dish.
After 15 minutes, take dough out of the bowl and flatten slightly with the palm of your hand. Cut dough into 8 equal sections. Roll each piece into a long rope, about 19-20 inches long. Shape dough into a pretzel shape and place in baking soda bath for 2 minutes. Once the 2 minutes is up, carefully pick up pretzel and place on prepared baking sheet.
Sprinkle the pretzels with the coarse sea salt while still wet. Repeat these steps until all 8 pretzels are prepared and on the baking sheets.
Bake pretzels for 8-9 minute or until golden brown. Immediately from the oven, brush heavily with the melted butter.
Notes
These are best served hot and fresh out of the oven, but will keep for about 2 days stored at room temperature in an airtight container.