In the bowl of a stand mixer, combine the active dry yeast, 1 teaspoon brown sugar, and ¼ cup warm water. Allow the mixture to rest for approximately 5 to 8 minutes, or until foamy.

In a separate bowl, stir together the remaining 2 tablespoons brown sugar and 1 cup warm milk until the sugar is fully dissolved.

Add 2½ cups of flour and the sweetened milk mixture to the yeast mixture. Attach the dough hook and knead at low speed for 5 to 7 minutes, or until the dough is smooth and elastic. If the dough remains sticky, gradually incorporate up to ½ cup of additional flour.

Transfer the dough to a lightly oiled large bowl, turn to coat, cover with plastic wrap, and allow to rise at room temperature for approximately 2 hours, or until doubled in volume.

On a lightly floured surface, divide the dough into four equal sections. Roll each into a 12×4-inch rectangle. With the long side facing you, press ¼ cup of shredded cheese into the lower third of the dough. Roll the dough tightly around the filling and slice into twelve 1-inch pieces. Repeat for remaining sections. Arrange pieces on a parchment-lined baking sheet.

Let the formed bites rest, uncovered, at room temperature for 30 minutes. Meanwhile, preheat the oven to 400°F.

In a large saucepan, bring 6 cups of water to a boil. Carefully stir in 4 teaspoons baking soda, then reduce heat to a simmer. Working in batches, gently place the pretzel bites seam-side down into the water. Boil each batch for 10 seconds, turn gently, and boil for an additional 10 seconds. Remove with a slotted spoon and return to the baking sheet.

Bake the pretzel bites in the preheated oven for approximately 15 minutes, or until golden brown.

While still warm, brush the baked pretzel bites with melted butter and sprinkle with coarse salt. Serve immediately, optionally with a dipping sauce such as honey mustard.