In a small bowl, combine 1 ½ cups of warm water, 2 1/4 teaspoons of active dry yeast, and 1 tablespoon of granulated sugar. Stir gently and let sit for around 5 minutes until frothy.

In a large mixing bowl, whisk together 4 cups of all-purpose flour and 1 teaspoon of salt. Gradually pour in the frothy yeast mixture and stir until a shaggy dough forms.

Transfer the shaggy dough onto a floured surface and knead for about 5 to 7 minutes until smooth and elastic.

Place the kneaded dough in a greased bowl, cover with a towel, and let rise for about 1 hour or until doubled in size.

Preheat your oven to 450°F (230°C) and line baking sheets with parchment paper.

In a large pot, bring 10 cups of water to a rolling boil, then add 2/3 cup of baking soda, stirring to dissolve.

Punch down the risen dough, divide into 8 pieces, and roll each piece into a 12-inch rope.

Wrap a slice of cheddar cheese around each hot dog and encase it completely with the dough.

Boil each wrapped pretzel dog in the baking soda bath for 30 seconds on each side, then place on the baking sheet.

Brush the tops with a beaten egg and sprinkle with coarse salt.

Bake for 12 to 15 minutes until golden brown.

Cool slightly on a wire rack and serve warm with mustard or dipping sauce.