Make the pretzels: Warm the milk in a saucepan until it's about 110 degrees; pour into a medium bowl.
sprinkle in the yeast. Let the yeast soften, about 2 minutes
stir in the brown sugar and 1 cup flour with a wooden spoon
Dice 2 tablespoons butter and soften; stir into the mix.
Add the remaining 1 1/4 cups flour and the fine salt to make a sticky dough. Turn the dough out onto a lightly floured surface and knead, adding more flour if needed, until smooth but still slightly tacky, about 5 minutes.
Shape into a ball, place in a lightly greased bowl and cover with plastic wrap. Let rise in a warm spot until doubled in size, about 1 hour.
Preheat the oven to 450 degrees and grease a large baking sheet. Punch the dough to deflate it, then turn out onto a lightly floured surface. (If the dough seems tight, cover and let rest until it relaxes.)
Divide the dough into 6 pieces. Roll and stretch each piece with the palms of your hands into a 30-inch rope, holding the ends and slapping the middle of the rope on the counter as you stretch. Form each rope into a pretzel shape.
Dissolve the baking soda in 3 cups warm water in a shallow baking dish. Gently dip each pretzel in the soda solution, then arrange on the prepared baking sheet and sprinkle with the coarse salt.