In a large bowl, stir together 1 cup of flour, yeast, sugar, 2 tablespoons of butter, and 1 1/3 cup water. Let this mixture stand until bubble begin to form, about 15 minutes. Stir in the salt and gradually stir in the remaining flour until dough can be picked up and kneaded on the counter. Knead until smooth and elastic, about 8 minutes, adding more flour if needed.
Divide the dough into 6 pieces and let them rest for a few minutes. Roll out one piece at a time into a rope about 15 inches long. Loop and twist into that cool pretzel shape. Set on a baking sheet while you roll out the remaining portions.
Preheat the oven to 450 degrees F (220 degrees C). Bring the remaining 3 cups of water to a boil and add the baking soda. Remove from the heat. Dip pretzels into the water bath for about 45 seconds, flipping over about halfway through. Place the soaked pretzels on a greased baking sheet. Brush them with melted butter and sprinkle with coarse salt.
Bake in the preheated oven until golden brown, 8 to 10 minutes.
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