In the bowl of a stand mixer, combine the yeast, 1 teaspoon brown sugar, and warm water and let rest 5-8 minutes until foamy.
In another bowl, stir together the remaining 2 tablespoons brown sugar and warm milk until dissolved.
Add 2 1/2 cups flour and milk mixture to the yeast. Attach the dough hook and knead dough at low speed until a smooth and elastic ball forms, 5 to 7 minutes. If dough is sticky, you can add up to an additional 1/2 cup flour.
Transfer the dough to a lightly oiled large bowl and turn the dough to coat with the oil. Cover with plastic wrap and let rise at room temperature until doubled in size, about 2 hours.
Turn out the dough onto a lightly floured surface. Divide into 4 equal pieces. Roll one of the four sections into a 12×4-inch rectangle.
With the long side facing you, gently press 1/4 cup of cheese into the bottom third of tRoll as tightly as possible, starting with the end that has the filling.
Cut into 12 1-inch pieces and transfer to a baking sheet lined with parchment paper. Repeat with remaining 3 portions of the douLet rest, uncovered, at room temperature for 30 minutes. Meanwhile, preheat oven to 400 F.
In a large saucepan, bring water to a boil. Add the baking soda and lower heat to a simmer. Carefully boil pretzels in batches, putting the pretzels into the poaching liquid, seam side down.
Poach for 10 seconds then carefully turn the pretzel over in the liquid. Poach other side for 10 seconds then remove with a slotted spoon to the same prepared sheet pans, seam side down. Repeat with the remaining pretzels.
Bake in preheated oven until golden-brown, about 15 minutes.
Brush warm pretzel bites with melted butter and sprinkle with salt. Serve warm with honey mustard dipping sauce.