In a small bowl or measuring jug, stir the warm water and barley malt syrup until dissolved.
In the bowl of a stand mixer (or a large bowl), whisk together the bread flour, instant yeast, and fine sea salt. Add the malted water and softened butter, then mix until a shaggy dough forms, 1–2 minutes.
Knead on medium speed (or by hand on a lightly floured surface) until the dough is smooth, elastic, and firm, 8–10 minutes.
Shape the dough into a ball, place in a clean bowl, cover, and let rise at warm room temperature until slightly puffy but not doubled, 45–60 minutes.
Turn the dough out and divide into 8 equal pieces. Working one at a time, roll each piece into a 24–28 inch rope with tapered ends and a thicker center. Form a U, cross the ends twice, and press the tips onto the lower curve to make a pretzel.
Arrange the shaped pretzels on parchment-lined baking sheets. Refrigerate uncovered until the surface feels slightly dry and the pretzels are firm, 20–30 minutes.
Meanwhile, preheat the oven to 450°F (230°C) with racks in the upper and lower thirds.
Prepare the lye bath in a well-ventilated area using nonreactive equipment (stainless steel or glass). Wearing gloves and eye protection, pour the cold water into a large stainless bowl. Slowly add the food-grade sodium hydroxide to the water (never the reverse), stirring until fully dissolved.
Using a slotted spatula, dip each chilled pretzel into the lye solution for 10–15 seconds, flipping once. Lift, let excess drip off, and return to the parchment-lined sheets.
Using a sharp blade, score a 3–4 inch slash across the thick belly of each pretzel about 1/4 inch deep.
Sprinkle pretzel salt generously over the pretzels. Bake 12–15 minutes, rotating sheets halfway, until the crust is deep mahogany brown and the slashed belly has opened.
Cool on racks for 10 minutes before serving. Handle any remaining lye solution carefully; store safely for reuse or neutralize and dispose according to manufacturer guidance.