Place ¼ cup water in a large bowl and sprinkle with yeast and sugar. Stir to dissolve and let yeast proof until bubbly, about 5 to 10 minutes. Add remaining cup water, 3½ cups of the flour, salt, and oil; stir to combine well. Turn dough out onto a lightly floured board and knead until smooth and elastic, adding the remaining ½ cup of flour as needed to prevent sticking. Lightly grease 2 heavy baking sheets with shortening. Divide dough into 24 pieces and roll each into a thin strip about 10 inches long. Shape into pretzels and place on prepared baking sheets. Cover pretzels loosely with towels and let them rest in a warm place until puffy, about 15 minutes. Lightly brush egg-milk glaze over the pretzels and sprinkle with salt. Bake at 425 degrees F for about 15 to 20 minutes, until lightly colored.