Make the broth: Bring 6 cups water and 1 teaspoon salt to a simmer in a medium saucepan over medium heat. Add the leeks and cook until tender, 3 to 4 minutes; remove with a slotted spoon to a bowl. Adjust the heat to keep the broth at a gentle simmer.
Meanwhile, heat 1 tablespoon butter in a wide saucepan over medium-high heat. Add the rice and cook, stirring, 1 minute. Add the wine and cook, stirring, until almost evaporated, about 1 more minute.
Add 2 cups of the hot leek broth to the rice; cook, stirring occasionally, until almost absorbed, about 6 minutes (adjust the heat to keep the risotto at a simmer). Add 1 more cup broth and cook, stirring, until almost absorbed, about 5 more minutes. Add the leeks, peas and 1 more cup broth and cook, stirring, until almost absorbed, about 5 more minutes. Taste the rice: If it is not fully cooked, add a little more broth and continue to cook, stirring, until al dente.
Stir in the ham and remaining 1 tablespoon butter. Remove from the heat; stir in 2/3 cup pesto, the mozzarella and Parmesan. Season with salt. Divide among bowls and top with the remaining pesto.