Bloom the yeast: in a white ceramic mixing bowl, stir together 1 cup warm water, 1 tablespoon sugar and the packet of yeast. Let it stand for 5 to 8 minutes, until the surface turns foamy; if nothing happens, the yeast is dead and you need a fresh packet.

Mix the dough: add 3 1/2 cups flour, 1 teaspoon fine salt and 1 tablespoon of the melted butter to the yeast mixture. Stir with a pale wooden spoon until a shaggy, sticky dough comes together and no dry flour remains at the bottom of the bowl.

Knead the dough: turn it out onto a lightly floured pale wood board and knead by hand for 5 to 6 minutes, until it turns smooth and elastic and springs back slowly when you poke it.

First rise: set the dough in a lightly buttered white ceramic bowl, cover with a damp towel, and let it rise in a warm spot for 45 to 60 minutes, until it has doubled in size and holds a dent when pressed.

Shape the bites: punch the dough down, divide it into 4 equal pieces, and roll each piece into a rope about 20 inches long on the wooden board. Cut each rope into 1-inch pieces; you should end up with roughly 24 to 28 bites.

Boil the bites: bring 10 cups of water and 2/3 cup baking soda to a rolling boil in the cream enameled Dutch oven. Working in batches of 6 to 8, boil the bites for 20 to 30 seconds each; they will float and look slightly puffed and matte. Lift them out with a slotted spoon onto a parchment lined white ceramic baking dish.

Finish before baking: brush each boiled bite with the beaten egg and scatter the coarse salt evenly over the tops. Arrange them with a little space between each one; at this point they still look pale and soft.

Bake the bites: slide the dish into a 425 degree F oven and bake for 12 to 15 minutes, until the bites turn deep mahogany brown on top and sound hollow when you tap one.

Cool slightly: let the bites rest on the baking dish for 5 minutes while you start the dip; they will firm up just enough to hold their shape without turning tough.

Make the roux: melt 3 tablespoons butter in the cream enameled saucepan over medium heat. Whisk in 3 tablespoons flour and cook for 1 minute, stirring constantly, until it smells faintly toasted and loses its raw flour color.

Add the milk and beer: pour in 1 cup whole milk and 1 cup lager beer in a slow stream, whisking the entire time so no lumps form. Bring to a gentle simmer and cook for 3 to 4 minutes, until the mixture coats the back of a wooden spoon.

Melt in the cheese: reduce the heat to low and add the grated cheddar by the handful, whisking after each addition until fully melted before adding more. Stir in the Dijon mustard, garlic powder, Worcestershire sauce, cayenne and 1/4 teaspoon salt.

Serve: pour the warm dip into a white ceramic serving bowl and set it in the center of a platter. Arrange the warm pretzel bites around the bowl and serve right away, while the dip is still glossy and pourable.