In a large bowl, combine the warm water (please see ingredient listing for specific temp/instructions) with one teaspoon of brown sugar and the packet of yeast. Let stand for about 7 minutes until foamy (see photo above). If your mixture does not foam, your water was probably not the right temperature and your yeast is not activated!
In a small bowl, pour the warm milk over the remaining two tablespoons of brown sugar and stir until the brown sugar is dissolved. When the yeast mixture is foamy, add the milk mixture and the flour and stir until combined into dough. On a clean, floured surface, knead the dough a few times with your hands and form into a ball. Lightly mist a large bowl with cooking spray and place the dough ball at the bottom (see photo above). Cover tightly with plastic wrap or aluminum foil and let sit for 2 hours until dough has risen and doubled in size (see photo above).
Line two large baking sheets with parchment paper and set aside. Split dough into four equal-sized balls. Also split diced ham and shredded cheese into four even piles. On a clean and lightly floured surface, roll one of the dough balls into a 12” x 4” rectangle, with the long side facing you. Sprinkle ¼ of the ham and ¼ of the cheese across the bottom third of the dough. Starting with the filled bottom end, tightly roll the dough over the filling into a tube shape and lightly press down the outer edge. Cut the dough roll into 12 equal pieces (about 1” each) and place them on the prepared baking sheet (see photo below). Repeat with the remaining ingredients. You should have 48 pieces. Let pieces sit, uncovered for 30 minutes. Preheat the oven to 400 degrees.
In a medium pot, bring 6 cups of water to a boil. Add the baking soda and reduce to a simmer. Using a slotted spoon, add the pretzel bites a few at a time and boil for 20 seconds, flipping once halfway through. Pretzels will puff up during this step. Use the slotted spoon to drain the water off and return the pretzel bites to the baking sheets.
Bake the boiled pretzel bites in the oven for about 15 minutes until golden brown. Remove from the oven and brush the pretzel bites with the melted butter. Sprinkle with salt and serve! I recommend serving with a dish of mustard for dipping.