Stir the warm water, yeast, and sugar in a large mixing bowl. Let stand for 5 to 10 minutes, until creamy and foamy.
Add the olive oil, salt, and 3 cups bread flour. Mix until a shaggy dough forms. Add the remaining flour a tablespoon at a time only if the dough is very sticky.
Knead for 8 to 10 minutes by hand, or 6 to 7 minutes with a dough hook on medium-low speed, until the dough is smooth, elastic, and slightly tacky.
Place the dough in a lightly oiled bowl and turn to coat. Cover and let rise in a warm place for 60 to 75 minutes, until roughly doubled.
Line a baking sheet with parchment and dust lightly with cornmeal. Divide the dough into 4 equal pieces. Shape each piece into a tight, smooth round and arrange seam-side down on the sheet.
Cover the rounds loosely and let rise for 25 to 35 minutes, until puffy. Meanwhile, heat the oven to 400°F (205°C).
Beat the egg with 1 teaspoon water. Brush the dough rounds evenly with egg wash, then score a shallow X across each top with a sharp knife.
Bake for 22 to 26 minutes, rotating the pan once, until the loaves are deeply golden and sound hollow when tapped on the bottom. Transfer to a wire rack and cool completely.
Cut a circle about 1 inch inside the edge of each loaf and lift off the lid. Remove the interior, leaving walls and a base about 3/4 inch thick. If desired, brush the inside lightly with olive oil and toast at 400°F for 5 minutes. Fill with thick hot soup immediately before serving.