In a small saucepan, heat the water and butter over medium heat until an instant-read thermometer registers between 110°F/43°C and 120°F/49°C. Slowly add the warm water mixture to the flour mixture in the stand mixer bowl and combine with a spatula until shaggy dough forms. Sprinkle in scallions.

To knead dough, turn machine to speed 2 and let knead until a soft, sticky dough forms, about 5–7 minutes, stopping to scrape the bowl and hook if needed. If dough is too sticky, add up to remaining ¼ cup (31 grams) flour, 1 Tbsp. (8 grams) at a time while continuing to knead on speed 2. 

Turn dough out onto a lightly floured surface, and shape into a smooth, round ball. Clean the bowl and rub lightly with oil. Return the dough to the bowl, turning to grease the top, and cover with plastic wrap. Let the dough rise in a warm place until it doubles in size, about 40 minutes.

Preheat the oven to 375°F/190°C. Lightly oil a 9-inch cast-iron skillet. Turn the dough out onto a lightly floured surface. Divide dough into 16 equal portions, and roll into balls, pinching seams to close. Cover and let rise until an indentation remains after lightly pressing the top of dough, about 25 minutes.

Bring water and baking soda to a boil in a medium saucepan. Carefully place two balls of dough into boiling water mixture. Cook for 30 seconds, flip, and cook for 30 seconds more. Use a spider strainer or slotted spoon to remove from water, allowing excess water to drip off before placing side by side in the prepared skillet. Continue until all dough balls have been boiled and placed in skillet.

Make the egg wash by whisking together the egg yolk and water with a fork. Brush the tops of the dough with egg wash. Using a pair of kitchen shears, snip a small “X” on the top of each pretzel and sprinkle with salt. Bake 16–20 minutes, or until the bread is golden brown. Serve warm.