Combine 4 cups bread flour, beer, water, shortening, yeast, brown sugar, salt, garlic powder, and onion powder in the bowl of a stand mixer fitted with a dough hook attachment. Mix, adding remaining flour a little at a time, until dough pulls away from the sides of the bowl and forms into a ball, about 2 minutes.
Lightly grease a large bowl with 1 teaspoon olive oil. Add dough. Cover with a clean towel and let rise until doubled in size, about 1 hour.
Grease 2 pizza pans with remaining 2 teaspoons olive oil; dust with cornmeal.
Punch dough down gently and divide into 2 portions. Place dough on the prepared pans. Cover and let rest, about 5 minutes. Stretch dough out 1 inch past the edge of the pans.
Arrange 8 sticks of cheese, ends touching, around the edge of 1 pan. Fold overhang over cheese and press dough to seal. Repeat with second pan.