Linguine with Leeks, Radicchio, and Walnut Pesto

Katie and I made this yesterday evening for dinner, using radicchio from my CSA box and parsley and lemon from the garden. It was easy, relatively quick, and delicious (though it did need a fair bit of seasoning, particularly with salt). It would also stand up well, I think, to additions and substitutions: garlic, crushed red pepper, pancetta if you're so inclined, lemon zest in the pesto, and so on. Katie was tasked with making the pesto, and she was rather heavy-handed with the cheese and walnuts, so this version will differ a bit from what's written up at the link.

Linguine with Leeks, Radicchio, and Walnut Pesto
Serves 2-3, or more as a side dish

8 ounces linguine or other noodly pasta
5 tablespoons extra-virgin olive oil, divided
3 cups thinly sliced leeks, white and light green parts only
1/2 cup (packed) fresh Italian parsley leaves
1/2 cup grated Parmigiano Reggiano, plus more for serving
1/3-1/2 cup walnut pieces (1.5-2 ounces)
2 teaspoons fresh lemon juice
2 cups thinly sliced radicchio
Salt and freshly ground pepper

Cook pasta in a large pot of boiling, salted water until al dente. Drain pasta, reserving 1 cup cooking liquid.

Meanwhile, heat 2 tablespoons oil in a large skillet or pot (one with a lid) over medium-high heat. Add leeks and season generously with salt and pepper. Cover and cook until leeks are tender and beginning to brown, stirring occasionally, about 10 minutes.

While the leeks cook, puree parsley, cheese, walnuts, lemon juice, and 3 tablespoons oil in food processor until coarse paste forms. Season pesto with salt and pepper. Add pasta, pesto, and radicchio to leeks and toss to combine, adding cooking liquid by tablespoonfuls if dry. Garnish with extra Parmigiano and serve.