In a large bowl, combine warm water, yeast, and sugar, stir, and let sit for 5 minutes until foamy.

Add kosher salt, melted butter, and 2 1/2 cups of the flour to the bowl, then stir until a shaggy dough forms.

Turn the dough onto a lightly floured surface and knead for 5 to 7 minutes, adding the remaining flour as needed, until smooth and slightly springy.

Lightly grease a clean bowl with butter, place the dough inside, turn to coat, cover, and let rise in a warm place until doubled in size, about 45 to 60 minutes.

While the dough rises, pat the hot dogs very dry with paper towels and cut the cheddar into 8 even sticks to fit alongside the hot dogs.

In a large pot, bring 6 cups of water to a simmer, then carefully stir in the baking soda until dissolved; keep at a gentle simmer.

Preheat the oven to 425°F and line a baking sheet with parchment paper.

Punch down the risen dough and transfer it to a lightly floured surface, then divide into 8 equal pieces.

Roll each piece of dough into a rope about 15 to 18 inches long.

Place a cheese stick alongside each hot dog, then starting at one end, wrap a dough rope around each hot dog and cheese, spiraling down and slightly overlapping the dough.

Carefully dip each wrapped pretzel dog into the simmering baking soda bath for about 30 seconds, then remove with a slotted spatula and place on the prepared baking sheet.

Brush each pretzel dog with the beaten egg wash and sprinkle the tops with coarse salt.

Bake for 12 to 15 minutes, or until deep golden brown and the cheese is just starting to ooze at the ends.

Remove from the oven and let cool on a wire rack for 5 to 10 minutes before serving.