In a medium microwave-safe bowl, heat the milk for 1 minute, or to about 110 degrees.
Pour into a large mixing bowl, and sprinkle the yeast over the milk.
Let stand 5 minutes, or until yeast is foamy and dissolved.
With a wooden spoon, stir in brown sugar, flour, butter, and salt, until just combined.
Fit the mixer with a dough hook attachment, and beat on medium speed for 2-3 minutes, or until dough is soft, smooth, and elastic. It should come together in a ball, but be slightly tacky. Add more flour, one tablespoon at a time, if dough is too sticky. You don't want it to be tough though - it should still be tacky and sticky.
Place dough in a greased bowl, turning over once to grease the top.
Cover and let rise in a warm place for 1 hour, or until nearly double in size.
Punch down dough, then turn out onto a lightly floured surface.
Cut the dough into 12 pieces - they will each be about the size of a baseball or a lemon.
Roll and stretch each piece of dough into 16-inch long ropes. Fold the ropes in half, pinch the edges, and twist both ends three times.
Dissolve the baking soda in 3 c. hot water - make sure it's thoroughly dissolved.
One at a time, gently dunk each pretzel in the baking soda solution.
Arrange pretzels onto parchment paper-lined baking sheets, about two inches apart.
Bake at 450 degrees for 9-12 minutes, or until edges are golden, and the centers feel set when lightly pressed.
Remove from heat, and immediately brush with melted butter.
Sprinkle with coarse sea salt.
Best served warm, but they reheat well in the toaster oven.