Weigh out 113 grams of discard and put it in the stand mixer bowl. Add 280 grams bread flour, the yeast, 1/2 tablespoon sugar and salt. Stir well, then stir in the butter and olive oil. Add ¼ cup of water and stir to soften dough. Continue adding water about a tablespoon at a time until most of the flour has been absorbed and dough doesn’t seem too dry or too sticky.
Put bowl with dough on stand mixer, attach dough hook and knead until dough is smooth and pulls away from the side of the bowl, approximately 4 to 5 minutes. Cover the bowl with plastic wrap and let sit in warm spot in the kitchen until doubled (45 minutes to an hour).
Preheat the oven to 450 degrees F. Line a half-sheet pan with parchment paper and spray with olive oil cooking spray or rub with vegetable oil. These pretzels can be sticky, even on parchment.
Bring the 5 cups of water and the baking soda to a rolling boil in a 3 1/2 quart saucepan.
Meanwhile, turn the dough and shape it into a long rectangle about 5x20 inches. Cut rectangle into 5 long even strips. Working one strip at a time, roll each strip with your fingers to make it cylindrical, then shape into a pretzel. Set the shaped pretzels on the parchment while you are waiting for the water to boil.
Once water starts to boil, lift the pretzel and gently drop into the gently boiling water. Boil for about 45 seconds. With a slotted spatula, lift pretzel (letting excess water drip off) and set on your parchment lined baking sheet. Repeat until you have boiled all five pretzels. With a pastry brush, brush with beaten egg and sprinkle with salt or Everything Bagel seasoning.
Bake until dark golden brown in color, approximately 12 to 14 minutes. Transfer to a cooling rack for at least 5 minutes before serving.