Rice and Pea Soup - Lidia

Ingredients

• 3 tablespoons extra-virgin olive oil plus more for serving
• 1/4 pound bacon (about 4 thick-cut strips) cut crosswise in 1/3-inch pieces
• 2 cups diced leek, in ½-inch pieces (about 6 ounces)
• 3 quarts water
• 1 tablespoon coarse sea salt or kosher salt or to taste
• 1 pound frozen peas (or 3 cups fresh peas, shucked)
• ¾ to 1 cup rice (short- or long-grain)
• 4 tablespoons chopped fresh Italian parsley
• Freshly ground black pepper to taste
• Freshly grated Parmigiano-Reggiano or Grana Padano for serving