Combine the yeast, brown sugar, warm water, and warm milk in a large bowl. Set aside until foamy, 5-8 minutes.

Add 2 ½ cups flour 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.

Spray a large bowl with oil. Transfer the dough to the bowl and roll it around to get all the sides oiled. Cover and let wise in a warm area for about an hour, until dough has doubled in size.

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 ¼ 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.

Preheat oven to 400F.

Bring 6 cups of water to a boil. Add the baking soda and reduce to a gentle simmer. Working in batches, boil pretzels, cooking about 20 seconds each, turning halfway through. They should be slightly puffed. Use a slotted spoon to drain the water and transfer to a parchment-covered baking sheet.

Bake about 15 minutes or until golden and puffed. Remove and brush the warm pretzels with melted butter and sprinkle with salt. Serve warm.