In a small bowl, mix together yeast, sugar, and warm water. Let stand until foamy and creamy, about 10 minutes. Add oil to the yeast mixture. Set aside.

In a stand mixer bowl or large bowl, combine flour and salt.

Pour yeast mixture into flour mixture and knead on low speed for 10 minutes. (If mixing it by hand, knead the dough for the same amount of time.)

Lightly oil a large bowl. Place dough inside, turning to coat.

Cover with plastic wrap and let rise in a warm place for 1 hour, or until doubled in size.

While the dough rises, cut the cheese into 1-inch-long rectangular pieces. Cover the cheese to keep it from drying out. Set aside.

When the dough has risen, heat the oven to 450 degrees F. Cover a baking sheet with aluminum foil and spray foil with cooking spray. Set aside.

Turn dough out onto a lightly floured surface and divide into 8 equal pieces. Roll each piece into a rope and use a rolling pin to flatten it out.

Place cheese pieces along the middle of the dough, leaving a few inches of dough on each end without cheese. Pinch the dough tightly up around the cheese and roll it out until it is in a rope shape again. Twist into a pretzel shape.

In a large saucepan, bring baking soda and 4 cups of water to a boil, stirring until the baking soda is dissolved. Remove from heat.

Completely dip each pretzel in the baking soda solution for 10-20 seconds each. Using a slotted spatula, remove pretzels from the water and place them on a baking sheet.

In a small bowl, beat the egg with the remaining 1 tablespoon water until foamy. Brush egg mixture over the top of each pretzel and sprinkle with cheese or sea salt.

Bake for 8-10 minutes, until golden brown.