Kosher salt
1 large russet potato (about 12 ounces), peeled and cut into 1/4-inch dice
2 medium carrots, peeled and cut into 1/4-inch dice (about 3/4 cup)
3 ounces string beans, trimmed and cut into 1/4-inch dice (about 3/4 cup)
1/2 small fennel bulb, trimmed and cut into 1/4-inch dice (about 1/2 cup)
1 small red onion, cut into 1/4-inch dice (about 3/4 cup)
1 pound dried penne
2 to 4 medium cloves garlic, minced (see note)
3/4 cup extra-virgin olive oil (see note)
1/4 cup minced parsley
Freshly ground black pepper
Grated Parmigiano-Reggiano, for serving
In a medium pot of salted boiling water, cook potato until a piece is easily crushed between fingers, about 5 minutes. Using fine strainer, transfer to large mixing bowl. Working one vegetable at a time, continue by boiling carrots, string beans, fennel, and onion until each is well done, about 5 minutes each; add each vegetable to mixing bowl as it is ready.
Add penne to boiling water and cook until al dente, following timing on package. Drain, reserving 1 cup of cooking water.
Meanwhile, add garlic, olive oil, and parsley to vegetables, and mix thoroughly until potatoes have broken down for form a chunky puree. Season with salt and pepper.
Add penne and a healthy grating of Parmigiano-Reggiano to vegetable sauce and stir to combine, adding cooking water 1 tablespoon at a time if sauce is too thick. Spoon into bowls, top with additional grated cheese, and serve.
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