Activate the Yeast: In a medium bowl, combine 1 1/2 cups of warm water at 110°F, 1 packet of active dry yeast, and 1 tablespoon of granulated sugar. Stir gently and let it sit for about 5 minutes.

Prepare the Dough: In a large mixing bowl, whisk together 4 cups of all-purpose flour and 1 teaspoon of salt. Pour in the yeast mixture from Step 1 and stir until a shaggy dough forms.

Let the Dough Rise: Place the kneaded dough into a greased bowl, cover it, and let it rest in a warm area until it has doubled in size, approximately 1 hour.

Preheat the Oven and Prepare Pans: Preheat your oven to 450°F (230°C) and line two baking sheets with parchment paper.

Boil the Water Bath: In a large pot, bring 10 cups of water to a boil. Stir in 2/3 cup of baking soda until fully dissolved.

Shape the Pretzel Dogs: Punch down the dough, divide it into 8 pieces, roll each into a rope, wrap around a hot dog and cheese slice, sealing the ends.

Boil the Wrapped Dogs: Place each wrapped hot dog into the boiling solution, boil for about 30 seconds on each side, and remove with a slotted spoon.

Arrange and Brush with Egg Wash: Transfer boiled pretzel dogs to prepared sheets, brush with beaten egg for a glossy finish, and sprinkle with coarse salt.

Bake to Perfection: Bake for 12 to 15 minutes until golden brown and cheese is bubbling.

Cool and Serve: Allow to cool slightly on a wire rack, then serve warm with your favorite dipping sauces.