Make the flour paste

• Bring the water to a simmer in a saucepan.
• Mix in the flour until you have a thick paste.
• Let it cool until just barely warm.

Bloom the yeast

• Dissolve the yeast in the warm water.
• Let it sit until frothy; if it doesn't foam, the yeast is inactive.

Combine the dough

• Add the cooled flour mixture to the yeast mixture.
• Add the sugar, salt and oil.
• Gradually mix in the remaining flour, one cup at a time.

Knead the dough

• Knead with a dough hook until smooth, elastic and pulling away from the sides of the bowl.

Rest and divide

• Let the dough rest.
• Divide it into 4 equal pieces.

Shape the loaves

• Roll each piece into a long, flat rectangle, using as little extra flour as possible.
• Starting from a long edge, tightly roll it into a log.
• Pinch the seam and the ends closed, then roll and shape until uniform.

Proof the loaves

• Place seam-side down on a parchment-lined baking sheet.
• Lightly brush the tops with oil and loosely cover with plastic wrap.
• Let rise until roughly doubled in size; go by volume, not the clock.

Score and first bake

• Preheat the oven to 375°F (190°C).
• Score the tops of the loaves with a sharp knife.
• Bake for 10 minutes.

Prepare the topping

• Mix the cheddar, mozzarella, Parmesan and Italian seasoning.
• In a separate bowl, beat the egg with a splash of water.

Top and finish baking

• Brush the loaves generously with egg wash.
• Pile on the cheese mixture.
• Return to the oven until baked through and golden.

Cool and serve

• Let the bread cool before slicing.
• Fill with your favorite sandwich ingredients.