Add water/beer to a small bowl and stir in brown sugar and yeast until fully incorporated; set aside for 5-10 minutes until mixture begins to foam. Chef’s Note: If the yeast mixture does not foam, the yeast may not be fresh and/or the water/beer was too hot or cold. Use a thermometer to achieve the perfect temperature of 105-110 degrees Fahrenheit.
Measure flour in a medium bowl and whisk in salt. In a large bowl, combine 1 1/2 cups of the mixture with the foaming liquid and 1 tablespoon of butter. Mix until a smooth batter forms.
Add an additional 1 1/2 cups of flour and salt mixture to batter and knead into a smooth ball, adding the remaining flour as necessary.
Place the dough in an oiled medium bowl, rotating the ball to lightly coat it with oil.
Cover and leave in a warm place for about 1 hour, until doubled in size.
Preheat oven to 400 degrees Fahrenheit; punch down dough and put onto a lightly greased surface. Divide into 8 equal pieces and roll into balls, then cover and let rest for 10 minutes.
Line a baking sheet with parchment paper and grease it with butter and/or oil. Melt remaining 3 tablespoons of unsalted butter in a small pan.
Using a rolling pin, roll one ball at a time into an oval the length of a hot dog.Place the hot dog in the center of the dough oval as your guide. Cut 8 strips perpendicular to the hot dog on the right and left sides of the oval.
Starting at the bottom, lace the left and right strips up around the hot dog to meet in the middle and press together gently. Continue with the remaining dough strips until the hot dog is enclosed in dough. Place on greased baking sheet and repeat with remaining dough and hot dogs.
Carefully dip the dough-covered hot dogs in the prepared baking soda bath and return to greased baking sheet. Sprinkle to taste with salt and bake at 400 degrees Fahrenheit in oven for 10 minutes.
Remove tray from oven and brush the pretzel dogs with the melted butter. Place tray back into the oven for an additional 8-12 minutes until golden brown.