In a stand mixer fitted with the dough hook, combine the warm water, brown sugar, yeast and butter. Mix until combined and let sit for 5 minutes.

Add the salt and flour and mix on low speed until combined. Increase to medium and knead until the dough is smooth and pulling away from the sides of the bowl, about 4 minutes. Add additional flour, a tablespoon at a time, if the dough appears too wet and sticky. Remove the dough and knead into a ball on a lightly floured surface.

Oil a bowl with vegetable oil, add the dough and turn it in the bowl to lightly coat it with oil. Cover with a clean towel and place in a warm spot for about one hour, until the dough doubles in size.

Once the dough has doubled in size, preheat the oven to 425. Grease a baking sheet or line it with a silicone mat, set aside.

Bring the water to a boil in a large pot and slowly add the baking soda.

Place the dough on a flat, lightly floured surface and divide it into 8 equal pieces. Roll each piece into a rope measuring about 20 inches. Cut the rope into 1 to 2 inch pieces. Boil the pieces in the baking soda water in batches (I did one rope worth of pieces at a time). Boil for 30 seconds and remove the pieces with a slotted spoon. Place them onto the prepared baking sheet, making sure they are not touching. Brush the tops with the beaten egg and season liberally with coarse salt. Bake in the oven for 15-17 minutes, until golden brown and cooked through. Serve with cheese sauce, mustard or any other dip you like.

In a saucepan over medium heat, melt the butter. Once melted, whisk in the flour and cook for a minute or two. Slowly add the milk while whisking. Bring to a simmer and cook until the milk has slightly thickened. Add in the cheddar and cream cheese and whisk until the cheese has melted and the sauce is smooth. Season to taste with salt and pepper.