Heat an outdoor grill, or proceed with the indoor instructions below.
Clean the leeks: remove the dark green sections and halve the leeks lengthwise. Under running water, gently rinse the leeks, pulling apart the layers to wash away any grit that’s gotten caught in them. Transfer to a work surface and brush lightly with olive oil.
Cook the leeks, outdoors: grill the leeks cut-side down until nicely charred, about 5 minutes. Flip them and lower the grill cover so they steam all the way through. When tender, remove to a work surface (about 5 more minutes).
Cook the leeks, indoors: heat a large cast iron or heavy-bottomed skillet over a high flame. Place the leeks cut-side down and cook until nicely charred, about 5 minutes. Flip them and cover the pan so they steam all the way through. When tender, remove to a work surface (about 5 more minutes).
When cool enough to touch, roughly chop the leeks and transfer to a food processor or blender along with the herbs, lemon juice, sea salt, 1/4 cup almonds, and 1/4 cup olive oil. Puree until smooth, adding more olive oil until you reach the consistency of ranch dressing.
Meanwhile, cook the pasta according to package directions, reserving 1/4 cup of starchy cooking liquid. Drain the pasta and transfer to a mixing bowl. Add the leek pesto and toss to combine, adding a splash or two of cooking liquid to thin the pesto if it’s gotten too thick or dry.
Transfer the pasta to serving bowls or a platter and top with the remaining almonds (coarsely chopped, if you like).