Bring 5 cups water to boil in heavy large saucepan over high heat.

While waiting for the water to boil, make the frizzled leeks.

Cut leeks lengthwise into thin strips. In a bowl of water wash leeks and drain by lifting leeks from water into a colander. Dry leeks very well between layers of paper towels.

In a saucepan at least 3 1/2 inches deep heat 1 inch oil.  Working in very small batches fry leeks (oil will bubble up quite high) until golden, about 10 to 15 seconds, transferring with a slotted spoon to paper towels to drain. Season frizzled leeks with salt. Leeks may be fried 1 day ahead and kept in an airtight container at room temperature.

Back to the water.  Gradually whisk in polenta, then 1 1/2 teaspoons coarse salt. Reduce heat to medium-low; simmer for a minute then add pesto, mix and simmer until polenta is tender, thick, and creamy, whisking often and adjusting heat to maintain gentle simmer, 15 to 20 minutes.  Season to taste with salt and pepper and spoon onto plate or bowl.