Place the pumpkin seeds in a dry 10-inch skillet over medium heat. Stir constantly for 4 to 5 minutes until the seeds start to pop and turn golden. Remove from heat immediately and spread on a plate to cool for 5 minutes.

Set aside 2 tablespoons of toasted seeds for garnish. Use the rest for the pesto.

Bring a large pot of water to a rolling boil. Add 1 tablespoon of salt, then add the pasta.

Cook according to package instructions until al dente, usually 9 to 11 minutes for linguine. Before draining, scoop out 120 ml (about 1/2 cup) of pasta cooking water and set it aside.

Drain the pasta and return it to the pot. Do not rinse it.

Add the cooled toasted pumpkin seeds, basil, Parmesan, garlic, lemon juice, lemon zest, salt, and black pepper to a food processor or blender.

Pulse 5 to 6 times to break everything down roughly. With the motor running, pour in the olive oil in a slow, steady stream and blend until the pesto is mostly smooth but still has a little texture. Scrape down the sides and taste for seasoning.

Take the pot with drained pasta off the heat. Add the pesto and toss to coat, adding pasta cooking water a splash at a time until the sauce coats every strand evenly and looks glossy.

Divide into four bowls. Scatter the reserved toasted pumpkin seeds over each portion, add shaved Parmesan, and finish with a little lemon zest if you like. Serve straight away.