Remove the tough leafy greens from the leeks and discard. Trim off and discard the roots of the leeks. Slice the bodies of the leek in half lengthwise and rinse under cold water. Peel back the layers to scrub out all of the dirt. Once clean, slice the leeks into thin half-moons crosswise. You can add the slices to a sieve and rinse them again under cold water to ensure any grit and dirt have been removed.
Sauté the leeks:
Heat 1 tablespoon extra virgin olive oil in a large pot over medium-high heat. Once hot, add the leeks and cook for 5 minutes until they soften. Season with salt and pepper.
Cook the aromatics:
Add the celery, garlic, and thyme to the leeks. Sauté for 3 minutes. Add the potatoes and toss to coat. Cook for 1 minute and then season with salt and pepper.
Toast the rice:
Add the rice to the pot and sauté for 1 minute to toast it lightly.
Simmer the soup:
Pour the water into the pot and bring to a boil. Add a generous pinch of salt. Reduce heat to low and simmer, uncovered, for 30 minutes or until the rice is tender. Taste and season once more with salt and pepper.
Prepare the cheese:
Place the cheese and cornstarch in a large bowl and toss to coat.
Add the cheese to the soup:
Add the cheese to the soup and stir to incorporate. Continue stirring until the cheese is completely melted. Taste and adjust the seasonings to your preference. Turn off the heat.
To serve:
Ladle the soup into bowls. Finish with grated pepperjack or more grated cheddar cheese. Garnish each bowl with a sprinkle of minced parsley. Enjoy!
Notes
Note 1: I used medium-grain white rice, but I've also made this with long-grain white rice. Any white rice, like jasmine or basmati, will work here. You could also use short-grain white rice like arborio.