In a small bowl, dissolve the yeast in lukewarm water and let it sit for about 5 minutes until frothy.

In a large mixing bowl, combine melted butter, brown sugar, and salt. Add the yeast mixture and stir well.

Gradually add all-purpose flour until a sticky dough forms; keep mixing until it pulls away from the bowl.

Knead the dough on a lightly floured surface for about 2 minutes until smooth and elastic.

Shape the dough into a ball, place in a greased bowl, cover, and let it rest for 10 minutes.

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

Boil 8 cups of water and add baking soda. Cut rested dough into pieces and shape into pretzels.

Boil each pretzel in the baking soda bath for 20 seconds, remove with a slotted spoon, and place on baking sheets.

Brush each pretzel with beaten egg and sprinkle with coarse salt. Bake for 12-15 minutes until golden brown.

In a saucepan, heat whole milk over medium heat until small bubbles form.

Melt butter in a separate bowl, whisk in flour to make a roux, and gradually add warm milk, stirring until thickened.

Stir in sharp cheddar cheese until melted and smooth.

Serve warm pretzels alongside the cheese dip for a delightful snack.