In a small bowl, whisk together 1 ½ cups warm water, 1 tablespoon brown sugar, and the yeast. Let stand until foamy, about 5 minutes.

Combine 4 cups flour, the kosher salt, and melted butter in a stand mixer bowl. (If you’re making the dough by hand, see step 3.) Add yeast mixture and beat with a dough hook on medium speed until dough is smooth and pulls away from the inside of the bowl, 4-5 minutes. (The dough will still be a little sticky.) Turn dough out onto a lightly floured surface and knead until the dough is smooth and springs back when pressed, 4-5 minutes longer, adding flour as required to prevent sticking.

To make the dough by hand, combine flour mixture in a large mixing bowl. Gradually stir in yeast mixture, then transfer dough to a work surface and knead until smooth and elastic, 8-10 minutes, adding flour as required to prevent sticking.

Oil the stand mixer bowl or mixing bowl (no need to wash it), place the dough in it, and turn it over. Cover and let rise in a warm place, free from drafts, until the dough is doubled in volume, 1-1 ½ hours.

Turn out dough onto a clean work surface and divide into 8 equal pieces. Working with floured hands and with one piece at a time, roll the dough into an 18-inch rope. Make an upside-down U shape and twist the ends twice. Holding onto the ends, lift them up onto the curve of the U” and press down to form a pretzel shape. Repeat the process with the remaining pieces of dough. Cover the pretzels with a kitchen towel and let stand until puffy, 20-30 minutes.

Preheat the oven to 450°F. Line 2 sheet pans with parchment paper or nonstick silicone mats.

When the pretzels have nearly finished rising, bring 8 cups water to a boil in a 5- to 6-quart stockpot or Dutch oven. (It may seem like a large pot for the amount of water, but you’ll need the extra volume to prevent the water from overflowing when you add the baking soda.) Add baking soda and the remaining 2 tablespoons brown sugar. Use your fingers to carefully lower one pretzel into boiling water without splashing. Boil, turning once with a slotted spoon, until pretzel is puffy and puckered, 20-30 seconds per side. Lift out pretzel and drain, then transfer to a prepared sheet pan. Repeat with remaining pretzels.

Combine egg yolks and remaining 2 teaspoon water in a small bowl. Brush egg wash on pretzels and sprinkle with coarse salt.

Bake pretzels until nicely browned, switching pan positions halfway through, about 12 minutes total. Transfer pretzels to cooling racks. Serve pretzels warm or at room temperature with your favorite mustard.