Warm the milk in a small saucepan until it's 110°F or warm it in a microwave for about 30 seconds; pour it into a medium bowl and sprinkle in the yeast. Let the yeast soften, about 5 minutes.
Stir in the brown sugar and 1 cup of the flour with a spoon. Melt 2 tablespoons of the butter and stir into the mix. Add the remaining 1 ¼ cups flour and fine salt to make a sticky dough. Add more flour if necessary to form dough into a ball. Turn 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 clean, 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°F. Line a large baking sheet with parchment paper and spray with nonstick cooking spray.
Punch the dough to deflate it, then turn out onto a lightly floured surface. Divide the dough into 6 equal 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 into a pretzel shape – form a U-shape, then holding the ends of the rope, cross them over each other and press firmly onto the bottom of the pretzel.
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 a prepared baking sheet and sprinkle lightly with coarse salt. Bake until golden, 10 – 12 minutes. Melt remaining 3 tablespoons butter and brush on baked pretzels. The pretzels are best enjoyed fresh on the same day.