In a mixing bowl, combine warm water, yeast, salt, and sugar. Let it sit for about 5 minutes until it becomes foamy. Gradually add the flour to the yeast mixture, mixing until a soft dough forms. Knead the dough on a lightly floured surface for about 5 minutes until it's smooth and elastic. Place the dough in a greased bowl, cover it, and let it rise in a warm place for about 1 hour or until it has doubled in size.
Preheat your oven to 450°F (230°C) and line a baking sheet with parchment paper. In a large pot, bring 10 cups of water and the baking soda to a boil. While the water is boiling, divide the dough into 12 equal portions. Roll each portion into a rope and shape it into a pretzel.
Carefully place the pretzels, one at a time, into the boiling water for about 30 seconds. Remove them with a slotted spoon and place them on the prepared baking sheet.
Brush each pretzel with beaten egg yolk and sprinkle with coarse salt.
Bake in the preheated oven for 12-15 minutes or until the pretzels are golden brown. Remove from the oven and brush with melted butter while they're still hot.
Allow the pretzels to cool slightly before serving. Enjoy your homemade Amish-style soft pretzels!