1 package (1/4 oz) active dry yeast (or instant yeast)
2 Tablespoons plus 1 teaspoon packed brown sugar, divided
1/4 cup warm water (110-115 degrees F)
1 cup warm milk (110-115 degrees F)
2 1/2 to 3 cups flour
1/2 cup finely chopped ham (about 3 ounces)
1/2 cup shredded cheese of choice (I used cheddar)
6 cups water
4 teaspoons baking soda
4 Tablespoons unsalted butter, melted
1-2 Tablespoons coarse salt
Combine the yeast, 1 tsp brown sugar, and warm water in a large bowl. Set aside until foamy, 5-8 minutes. (If using the instant yeast, you can skip this step and just add it to the flour.) In another bowl, stir together the remaining 2 Tbsp brown sugar and warm milk until dissolved.
Add 2 1/2 cups flour and milk mixture to the yeast. Stir with a wooden spoon until a soft dough forms. Add the remaining flour as needed. Turn the dough out onto a lightly floured surface and gently knead a few times, forming a smooth ball.
Brush the inside of a large clean bowl with olive oil. Transfer the dough to the bowl and cover tightly with plastic wrap. Allow to rise in a warm, draft free area for about 2 hours, until dough has doubled in size and bubbles appear on the surface.
Turn out the dough onto a lightly floured surface. Divide into 4 equal pieces. Lightly dust your hands and rolling pin with flour. Roll one of the four sections into a 12×4-inch rectangle. With the long side facing you, gently press 1/4 of the ham and cheese into the bottom third of the dough, and roll as tightly as possible, starting with the end that has the filling. Cut into 12 1-inch pieces and transfer to a sheet pan lined with parchment paper. Repeat with remaining 3 portions of the dough.
Let rest, uncovered, at room temperature for 30 minutes. Meanwhile, preheat oven to 400?F.
Bring 6 cups of water to a boil. Add the baking soda and reduce heat to a gentle simmer. Boil pretzels in batches, cooking about 20 seconds each, turning once. They should be slightly puffed. Use a slotted spoon to transfer them back to the baking sheets.
Bake until puffed and golden-brown, about 15 minutes.
Brush warm pretzel bites with melted butter and sprinkle with salt. Serve warm or at room temperature.