The first thing you'll do is bloom your yeast. Add your yeast and sugar to the warm water and stir. It should get foamy and smell like the most delicious beer in just about 6–10 minutes.
Now, combine your flour and salt. Next, add your yeast water mixture and the melted butter. Combine until a smooth dough forms. Once ready, add a bit of olive oil to a bowl and add your dough ball, making sure to rub it a bit with oil so that it doesn't form a crust. Cover with plastic wrap and a kitchen towel and let rise until doubled in size (about 2 hours). When I'm proofing my dough, I turn the oven light on (NOT THE OVEN!) and let it proof in there :)
First, take your dough out of the oven and preheat your oven to 450 degrees F and line a baking sheet with parchment paper. You'll also want to get ~8 cups of water on the stove and start bringing it to a boil.Now that your dough has doubled in size, punch it to deflate it in the middle and add to to your clean work surface. Divide the dough into 4 equal-ish parts. Now you're going to roll each piece to form a long rope. I make 4 pretzels with this recipe, but if you want smaller pretzels you can divide the dough into 6 or even 8 parts. Totally up to you. Now you're going to take your dough rope fold the end of each side in to the middle and over the other. Once you have this shape, you can leave it as is and press each side down, OR you can do what I do and twist the pretzel ends around once and then press the ends into the dough. Make sure you really press those ends into the pretzel so they weld together. If not, you run the risk of them popping off when they go into the baking soda bath. They'll still taste amazing though :) Add these to your parchment-lined baking sheet.
Now that the water is boiling, add the baking soda. DO THIS CAREFULLY! Baking soda reacts to water and will bubble up, so sprinkle in a little at a time so you don't absolutely terrify yourself like I did the first time. Whew.Once ready, add each pretzels and let them boil for about 45 seconds. I do 1–2 pretzels at a time. When ready, remove with a slotted spoon, pat with a paper towel and add back to the parchment lined baking sheet. Now, take your beaten egg and brush it on to each pretzel. Then, sprinkle some coarse salt on top.
Now, just bake your pretzels in your preheated oven for ~15–18 minutes or until they're a beautiful golden color. Remove from the oven, brush with some melted butter and enjoy!