Place the milk in a medium bowl and stir in the yeast to dissolve it well. Add the malt syrup and 1 cup of the flour and stir until you have a smooth batter. Sprinkle on the salt, add the butter, and stir well to incorporate. Add 1¼ cups more flour and stir and turn the dough to incorporate it. Turn out onto a floured surface and knead for 5 minutes, incorporating more flour as necessary.
Place the dough in a clean bowl, cover with plastic, and let rise for 1½ hours, or until smooth, softened, about doubled in volume.
Place a rack in the upper third of the oven and place a baking stone or unglazed quarry tiles, if you have them, (or a baking sheet) on it. Preheat the oven to 450°F.
Turn the dough out onto a very lightly floured work surface. Cut it into 4 equal pieces and cut each piece in half. Place a parchment paper-lined baking sheet next to your work surface.
Work with 2 pieces of dough at a time, keeping the remaining pieces covered with a cotton cloth. Roll each piece of dough out under your palms to a long skinny rope, 24 to 30 inches long, slightly fatter in the middle and very thin at the ends. Press down lightly and push outward toward the ends with both hands as you roll, encouraging the dough to lengthen and stretch. You will find the dough very elastic, and that it springs back and shortens after you let it go, so switch back and forth between the two pieces. This will give the gluten strands in the dough an opportunity to relax a little.
Once you have a long rope, pick up one end with each hand and twist one around the other once or twice about 2 inches from the ends, then lay the dough down in a curve on the baking sheet and lay the ends onto the fatter center of the curve to make the classic pretzel shape. Cover lightly while you shape the remaining pretzels. Let the pretzels rise for about 10 minutes.
Meanwhile, heat 1 cup water in a large saucepan until almost boiling. Add the baking soda and stir well to dissolve. Keep the water simmering until just before ready to use. Have a flour-dusted peel (or the back of a baking sheet) near your work surface, and a razor blade or sharp knife for slashing the dough.
Lift up one pretzel with a wide spatula and place it briefly in the hot soda-water bath, leaving it on the spatula. Remove it after 20 seconds and let the water drain off the spatula, then brush the pretzel top with the egg wash and place the pretzel on the peel. Make a deep Ito 2-inch slash in the top of the fattest part of the pretzel, then immediately slide it off the peel (or sheet) onto the hot stone or tiles (or baking sheet). Repeat with the remaining pretzels. (If your stone or oven is small, you may have to bake them 4 at a time.)
Bake the pretzels for 10 to 12 minutes, until a deep golden brown on top. Place on a rack to cool. Serve warm or at room temperature.