Measure the flour into a mixing bowl. Add the salt and the proofed yeast and 1 cup of warm water. Mix by hand or with a stand mixer with a dough hook until the flour mixture comes together into a stiff ball. Add water as needed to form a dough.
Knead for 5 minutes. Let rest for a few minutes and then add the butter. Knead for at least 5 more minutes or until the butter is fully incorporated. At this time, the dough should be firm and soft, velvety to the touch.
Form into a ball; butter all the surfaces and let rise until doubled, about 1 hour in a warm spot.
Wipe up spills with paper towels and dispose immediately. Rinse with water or vinegar. Rinse all the utensils and gloves with large amounts of water, and wash your arms and hands after working with the solution. If you feel anything burning on the skin, rewash with soap and water, rinse well and dry.
Place a wax paper on a baking sheet.
Punch the dough down and divide into 12 pieces (2-oz pieces). Form into balls. Using very little flour, form the balls into 1-foot long strands, thicker in the middle, and tapering towards the ends. (Using water makes the dough slightly sticky and helps with shaping.)
Take each strand and roll out again to form 2-foot strands. Twist into pretzel shape, using a little water again to make the ends stick to the loop.
Place the pretzels on the baking sheet and refrigerate for 1 hour. (This dries out the surface and makes them easier to handle.)
Meanwhile, make the lye solution. Don gloves and goggles. Place 1 quart of water in a plastic or glass container. Weigh 1 ounce of food-grade or reagent-grade sodium hydroxide into a bowl and add slowly to the water, stirring with a plastic spoon or similar object. (ALWAYS add the lye to the water. For scientists, the lye solution will be approximately 0.75 M NaOH (FW 39.99 g/mol) or almost 3% w/w.)
Remove the pretzels from the refrigerator and dip each for 30 seconds into the lye solution. Remove with a slotted spoon and place on a greased or parchment paper-lined baking sheet.
Sprinkle the pretzels with salt. Make a deep cut through the thick part of the pretzel horizontally with a razor blade or lamé. Let the pretzels rest for 15 minutes.
Heat the oven to 375°F. Bake the pretzels for 20 to 25 minutes, or until deep golden brown.