In the bowl of a standing mixer fitted with the dough hook attachment, combine the warm water, yeast, honey, and vegetable oil. Mix this up with a spoon or spatula (don’t turn on the mixer yet), and then allow it to sit until the yeast activates and starts to foam, about 10 minutes. Add the flour, salt, and melted butter, and turn the mixer on low. Knead the dough for about 5 minutes, until slightly sticky and pulling away from the walls of the bowl, forming a ball. Place the ball of dough into a separate well-oiled bowl and cover with a clean kitchen towel. Set in a warm place and let it rise until it doubles in size, about one hour.
Once the dough has been allowed to rise, preheat the oven to 450°F and prepare two baking sheets with parchment paper. Fill a large shallow pot with water and start it boiling on the stove as you work. This will be your water bath. Turn the dough out onto a clean, floured surface (I usually use a large silicone mat or wooden cutting board, but a clean counter works just as well). Knead the dough with your hands a few times, and break the dough into 4-6 manageable chunks. Roll each ball of dough into ropes about ½ inch in diameter. Cut the ropes into pieces about 3 inches long, and wrap each little hot dog in the strips of dough, smoothing or pinching the ends of the dough together. I like to wrap the strips of dough around the back and cross them over front, joining the ends again at the back. I think it looks nice aesthetically, but that certainly isn’t necessary.
Once the cocktail franks are prepared and the water is boiling, add the baking soda to the pot. Drop the prepared franks into the boiling water a few at a time, and boil each batch for 30-45 seconds. Remove with a slotted spoon and place on prepared baking sheets, a little space between each. Brush the tops with the egg wash mixture, and sprinkle each with salt. Pretzel salt can sometimes be hard to find or pricier as a specialty ingredient, so I usually just use plenty of coarse salt. Bake the mini pastry pigs for 10-15 minutes until golden brown.
In a medium-sized saucepan over medium heat, melt the butter. Whisk in the flour to make a simple roux. Cook for a minute or two, until the mixture thickens and turns a light golden color. Slowly pour in the bottle of hard apple cider and whisk continuously to distribute the roux throughout. Allow to boil for a few minutes until reduced slightly, stirring often. I like to use a silicone whisk, but a wooden spoon works too.
Reduce the heat to medium-low and add the dijon mustard and salt, and then add the shredded cheddar in handfuls. Stir often, making sure nothing sticks or burns to the bottom of the sauce pan, until the cheese melts and the mixtures thickens, 5-10 minutes. If you find the sauce is too loose or liquid, feel free to stir in 1 tsp cornstarch to help the process along. Once at the desired consistency, remove the pan from heat and stir in the brandy. Serve immediately alongside the Pretzel Pastry Pigs in a small bowl with a pinch of black pepper.