Warm the milk and 2 tablespoons of the butter in the microwave until the butter is just melted, about 90 seconds; do not boil. (Alternatively, warm the butter and milk in a small saucepan.)
Add the brown sugar and stir until dissolved; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, combine the flour with the yeast and salt.
Mix on low speed until well combined, about 1 minute.
With the mixer on low, gradually add the warm milk mixture to the bowl.
When the dough forms a cohesive mass, switch to the dough hook.
Knead, adding more flour as needed, until the dough is smooth but still slightly tacky, about 5 minutes.
Shape the dough into a ball, place in a clean, lightly greased bowl, and cover with plastic wrap.
Let rise in a warm spot until doubled in size, 1 to 2 hours.
Punch the dough to deflate it, then turn it out onto a clean work surface. Shape the dough into a log and cut into six equal pieces.
Roll and stretch each piece with the palms of your hands into a 24-inch rope, holding the ends and slapping the middle of the rope on the counter as you stretch.
Combine the baking soda with warm water in a 2-quart baking dish and stir until dissolved. Gently dip each “rope” into the soda solution. This alkaline solution is what gives the pretzels their signature dark brown, shiny crust and distinctive flavor. The solution causes a chemical reaction called the Maillard reaction, which results in browning and a distinctive taste. Without this step, the pretzels would not have the same taste, texture, or appearance that we associate with them.
Let any excess liquid drip off, then form the dough into a pretzel shape directly on the prepared baking sheet (form a U-shape, then holding the ends of the rope, cross them over and under each other — making a twist in the middle — and press the ends onto the bottom of the pretzel). Sprinkle evenly with the coarse salt.
Bake until golden, 8 to 12 minutes. Melt the remaining three tablespoons of butter and brush on the baked pretzels.
Enjoy the pretzels warm out of the oven, or reheat them in an oven or microwave.