Heat the milk until it reaches 110 F (43 C).
Pour the milk into the mixer bowl, equipped with a dough hook, and sprinkle the yeast.
Let the yeast soften for about 2 minutes, then mix in the brown sugar and 1 cup (125 g) of flour with a wooden spoon.
Melt 2 tablespoons of butter and mix it into the dough.
Add the remaining 1 and 1/4 cups (155 g) of flour and fine salt to form a sticky dough. Add more flour if necessary (you will probably need a few tablespoons) to form a ball of dough.
Knead until the dough is smooth and elastic, and no longer sticks to your fingers, about 5 to 8 minutes.
Shape the dough into a ball in a lightly oiled bowl, covered with plastic wrap.
Let it rise in a warm place until it doubles in volume, about 1 hour.

Preheat the oven to 425 F (210 C).
Line a large baking sheet with a silicone mat.
Punch down the dough, then place it on a lightly floured surface.
Divide the dough into 6 equal pieces.
Roll and stretch each piece into a 30″ (75 cm) long rope with the palm of your hands.

Shape each rope into a pretzel shape… Start by forming a U, then twist the two ends once, and fold the two ends over the curved part of the U.

Heat the water and baking soda. The water should not boil and should be just simmering.
Dip the pretzels in the water for 20 seconds and place them on the prepared baking sheets.
You will need to reshape the pretzels into their original form.
Sprinkle with coarse salt.

Bake for 10 to 12 minutes.
Brush with melted butter as soon as they come out of the oven.