In a small saucepan, bring 4 cups of water to a simmer; keep this "backup" water hot, covered, over medium-low heat. Bring the remaining water, the bay leaves, and 1 tablespoon salt to a boil in a 3-to-4-quart cast-iron saucepan, over medium-high heat. When boiling, add the olive oil.
Scoop up a small handful of the cornmeal, and, while stirring constantly with a wooden spoon or flat-ended stirrer, let it sift slowly through your fingers into the seasoned boiling water. Let the cornmeal fall a pioggia—like rain—into the water. Sift the remaining cornmeal into the water a small handful at a time, stirring constantly, paying special attention to stirring the corners of the pot. It should take about 5 minutes to add all the cornmeal.
When all the cornmeal has been added, the mixture should be smooth and thick and begin to "perk," with large bubbles rising to the surface. Reduce the level of heat to medium-low, and continue stirring until the mixture becomes too thick to stir easily, about 4 minutes. Add enough of the "backup" water—about 1 cup—to restore the mixture to a smooth stirring consistency. Stir until the mixture is again too thick to stir easily. Continue adding water and stirring like this until the cornmeal is tender, about 20 minutes after the cornmeal was added.
When the cornmeal is tender, stir the polenta without adding water until it is shiny and begins to gather around the spoon as you stir it, 5 to 10 minutes. (The polenta should be thick enough to stand a spoon in.) The polenta is ready to serve at this point, or you can choose to cook it an extra few minutes to intensify the flavor. To continue cooking, reduce the level of heat to low, and stir the polenta constantly for 5 to 10 minutes. You may need to add a small amount of water during this extra cooking if the polenta begins to stick or become too thick.
Pour the polenta away from you into a ceramic bowl. Let it stand 10 minutes before serving. To serve polenta, scoop it onto plates with a large spoon, dipping the spoon in water before each scoop. (An ice-cream scoop can be used in the same fashion; it makes nice round mounds of polenta.)
Polenta at the Table
For immediate serving: You may also serve the polenta hot directly from a board in the traditional way: Pour the hot polenta into the center of a wooden cutting board, keeping the polenta in a long, high mound. Let the polenta stand a few minutes, until it is firm enough to cut. Cut the polenta with a string stretched taut between your index fingers, or with a thin knife. Gently transfer the slices to plates.
To chill the polenta for baking, grilling, or pan-frying: You can begin to see the true versatility of polenta when it has been chilled until firm and cut into shapes for baking, grilling, or pan-frying. To serve polenta this way, pour the hot polenta—either freshly made for this purpose, or remaining from a batch made to be eaten hot—into a baking pan or mold to a thickness of about 1/2 inch. (One whole recipe of Basic Polenta makes enough to fill two 9-by-13-inch baking dishes to a depth of about 1/2 inch.) Cover with plastic wrap applied directly to the surface, and refrigerate until thoroughly chilled and very firm, 4 to 5 hours. Invert the polenta onto a cutting board and cut it into any desired shape for baking, grilling, or frying.
To bake: Place the polenta pieces on a lightly oiled baking sheet and place in a preheated 375° F oven until lightly browned and crispy, about 20 minutes. Turn the polenta once about halfway through the cooking.
To grill: Lightly brush both sides of the polenta pieces with olive oil. Place on a hot grill, and cook, turning once, until well marked and heated through, about 2 minutes per side.
To pan-fry: Heat a small amount of olive oil in a nonstick skillet over medium-high heat. Add the polenta slices, and cook, turning once, until golden brown and crispy on both sides, 8 to 10 minutes.