First, a large part of the credit goes to this recipe: http://www.wittyinthecity.com/2014/12/philly-style-soft-pretzels/, and also to the Philly Pretzel Factory website, which conveniently listed their actual ingredients and what a pro pretzel actually weighs. The rest was trial and error.
Now, my recipe:
Ingredients
425 g bread flour
1 tbsp dough conditioner (see note 1)
2 tsp kosher salt
2 tsp (or 1 packet) active dry yeast
1 cup warm water
Pretzel salt (see note 2)
Instructions
1. Turn on your oven with pizza stone or steel inside to 450F.
2. Mix the yeast with the water in your stand mixer bowl and let bloom for 5 minutes.
3. Mix the flour, salt, and dough conditioner together, then dump into the stand mixer bowl. Blend together with the paddle at low speed until it's largely incorporated, then switch to the dough hook.
4. Knead with the dough hook for 10 minutes to develop all of that chewy, addicting gluten.
5. Split the dough into 6 equal balls (use a kitchen scale for this, each ball should be about 110 g). Cover lightly with plastic wrap and let sit 30 minutes.
Baking soda method:
6 cups water
2 tbsp baking soda
1 egg yolk mixed with 1 tbsp water
6. Bring 6 cups of water to boil in a wide pan and dissolve the baking soda into it (I tried baked baking soda (sodium carbonate); the result wasn't worth the effort). I also found that a greater concentration of baking soda added a disgusting bitter taste, but feel free to experiment.
7. Press down on dough balls to remove large air bubbles and roll out to 20" lengths. Double-twist the ends and fold down, pressing the tips into the bottom of the U. Then stretch the sides to make the classic Philly shape. Stage on a silpat or parchment paper.
8. One at a time, float the pretzels into the boiling water for 30 seconds, flipping midway if you like. Replace onto parchment and brush with egg yolk wash. Make sure pretzels are close enough together to join while baking.
9. Sprinkle on pretzel salt, place gently on your steel/stone, and bake for 10 minutes.
Lye method:
1 oz food grade lye (see Note 3)
1 quart warm water
6. Add 1 quart water to a lye-safe plastic or glass bowl in your sink. Put on your gloves and goggles and weigh out 1 oz of lye in a lye-safe plastic or glass bowl on your kitchen scale. Avoiding any possible fumes, pour lye into water and stir gently until dissolved with a lye-safe plastic spoon/spatula. Rinse off the spoon and put in your sink (not on the counter!). Rinse gloves and remove (do not put down on counter!).
7. Press down on dough balls to remove large air bubbles and roll out to 20" lengths. Double-twist the ends and fold down, pressing the tips into the bottom of the U. Then stretch the sides to make the classic Philly shape. Stage on a silpat or parchment paper.
8. Put goggles and gloves back on and place pretzels, one at a time, into lye bath for 10 seconds a side. Then place back onto parchment. Pour lye down drain, rinse bowl, rinse and remove gloves.
9. Sprinkle on pretzel salt, place gently on your steel/stone, and bake for 10 minutes.
Note 1: dough conditioner is a dairy-based additive that reduces mixing time, makes the dough more pliable, and increases shelf life. I bought a 5-lb bag of https://www.bakersauthority.com/products/5lb-reddi-sponge-dough-developer-dough-conditioner-dairy, and it'll probably last a decade. Highly recommended.
Note 2: reasonably priced pretzel salt option here: https://www.walmart.com/ip/Hoosier-Hill-Farm-Coarse-Pretzel-Salt-2-lbs-plastic-jar/169450968
Note 3: I used this lye https://www.amazon.com/exec/obidos/tg/detail/-/B07KNR9SVF/stoobushblog-20