FOR DOUGH: In the bowl of a stand mixer, combine 2 cups of the flour and the yeast. In a saucepan, heat the milk, sugar, oil and 1 1/2 teaspoons of salt, just until warm. Stir constantly. Add to flour mixture. beat at low speed for 30 seconds. Scrape the bowl. Beat for 3 minutes on high speed. Stir in as much of the remaining flour as you can mix in with a spoon. If you have a kneading hook on your stand mixer, you can use it here. Put dough on a lightly floured surface and knead in enough of the flour to make it moderately stiff. You want it to be smooth and elastic. Shape into a ball. Place in a lightly greased bowl, turning once to grease the surface of the dough. Cover; let rise in a warm place until doubled in size, about 1 1/2 hours.
Punch down the dough. Place on a lightly floured surface. Cover; let rest for 10 minutes. Using a rolling pin (or something similar), roll out into a 12x8" rectangle.
Cut into 16 strips about 1/2" wide and 12 inches long.
Roll each strip into a rope about 16" long. Cut the strip into 2-2 1/2" sections. NOTE: If you decide to make pretzels, don't cut the strip, but shape it into a pretzel.
Once all the strips have been cut, let them rise again, uncovered, for 20 minutes.
Preheat your oven to 350 degrees and grease a baking sheet.
Bring water to a boil and dissolve 3 tablespoons of salt in it. Add a single layer of pretzel bites into the boiling water. They will float. Boil for 2 minutes, turning once. NOTE: Do not over cook in the boiling water. They will not turn out.
Remove the pretzels with a slotted spoon to a paper towel. Let stand a few minutes; then place on the greased baking sheet. Repeat until all the pretzels have been boiled. Whisk together the egg white and 1 tablespoon water. Brush over the pretzels.
Sprinkle with coarse sea salt. Bake 25-30 minutes or until light golden brown. Leave in longer if you like them darker brown. Brush with melted butter for some added flavor if desired.