Mix ⅔ cup water and ⅔ cup whole milk in a small saucepan and warm to 80-90°. Use an instant-read thermometer to make sure liquids do not get too hot. Liquid over 130° will kill the yeast.
Dissolve yeast in warm liquid, stir in. Allow to sit for 10 minutes until foamy.
Mix flour, salt, yeast mixture, and melted butter in a stand mixer bowl. Equip stand mixer with dough hook. Knead for five minutes on speed 2 (or the proper kneading speed for your mixer.) Speed 2 is recommended for a Kitchen Aid Stand Mixer. Dough should pull away from the side of the bowl cleanly and it will be slightly sticky, but should be soft and elastic.
Cover the bowl with plastic wrap (or a towel) and allow it to rise for 90 minutes or until doubled in size.
Preheat oven to 400° and prepare poaching liquid. Mix water, salt, brown sugar, and baking soda in a large pot and bring to a boil. (The brown sugar doesn't make the pretzels sweet, but cuts the bitterness of the baking soda.)
When properly prooved, turn dough onto a clean work surface and divide into 8 equal pieces of dough. Roll each piece into a rope and twist into a pretzel shape.
Poach pretzels two at a time for 2-3 minutes each, flipping halfway through. Gently remove pretzels with a slotted spoon and place on parchment-lined baking sheets.
Whisk egg yolk and 1 tsp water to make an egg wash. Brush over poached pretzels and sprinkle with fleur de sel (or coarse salt.)
Bake for 15-20 minutes until crust develops a deep color. If baking all 8 pretzels in one batch, rotate baking sheets halfway through. Place pretzels on a rack to cool. Serve with salted butter, mustard, or beer cheese. They are excellent warm, but also good at room temp or reheated in a toaster.