Heat 1 cup water and shortening until about 120 degrees. Add sugar and yeast and stir until dissolved. Let yeast proof for a few minutes (become bubbly)
In a large bowl combine flour, salt and crumbled bacon pieces. Add yeast mixture and blend at low speed until moistened, then beat 3 minutes at medium speed.
Stir in additional 1 1/4 to 1 1/2 cups flour until dough pulls cleanly away from the bowl.
On a floured surface knead in 1/4 cup to 1/2 cup flour for about 10 minutes until dough us smooth and elastic.
If you have a mixer with a dough hook, let it do the work and knead for about 5 minutes.
Clean the large bowl and grease it. Place the dough in the bowl, cover and let rise until doubled in bulk about 45-60 minutes.
Punch down dough to remove all air bubbles. Let rest 10 minutes.
Divide dough into 12 pieces. Roll into long ropes and shape like a pretzel, or cut into small "pretzel bites". Place on greased baking sheet. Let rise until light, 15-20 minutes.
Preheat oven to 400 degrees F. In a large saucepan, bring water and baking soda to a boil.
Add pretzels gently to the boiling water 2-3 at a time. Flip after 15 seconds and boil another 15 seconds. If you like them with extra pretzel taste, boil 30-45 seconds a side.
Remove pretzels with a slotted spoon and return to the baking sheet. Combine egg white with 1 tablespoon water and brush on pretzels. Sprinkle with parmesan cheese.
Bake for 8-10 minutes depending on desired level of brownness.