Combine the water, yeast, sugar, and salt in a large mixing bowl. Whisk with a fork until the yeast is dissolved. Mix in the flour 1/4 cup at a time, stirring with a large wooden spoon, until the dough comes away from the sides of the bowl and forms a ball. (Alternatively, this can be done with a heavy-duty electric mixer fitted with a dough hook. Combine the water, yeast, and sugar in the bowl of the mixer. Add the salt and 4 cups of the flour and, with the mixer on low speed, beat until combined. Add the remaining 1 cup flour and, with the mixer on high, mix until the dough climbs up the hook, about 3 minutes.)
Lightly oil a large bowl with the oil. Put the dough in the bowl and turn to oil on all sides. Cover the bowl with plastic wrap or a kitchen towel. Let stand in a warm, draft-free place until the dough doubles in size, 1 1/2 to 2 hours.
Sprinkle a large baking sheet with the cornmeal.
Turn the dough out onto a lightly floured surface and divide it into 20 pieces. One at a time, cup your hand over a piece of dough and gently push down on the dough while rolling it in a circular motion under your hand to form a smooth ball. Arrange the rolls about 1 inch apart on the prepared baking sheet. Cover with plastic wrap or a kitchen towel. Let stand in a warm, draft-free place until they double in size, about 30 minutes.
Preheat the oven to 400°F.
Brush the tops and sides of the rolls evenly with the egg glaze. Bake until golden brown, about 30 minutes. Cool for 10 minutes on the baking sheet, then serve warm.
Yield: 20 rolls