Toast 1/4 cup pine nuts in a dry skillet over medium heat until golden, 2 to 3 minutes. Keep an eye on them: they burn quickly.
Put 1 clove garlic, the toasted pine nuts and 1/4 tsp salt in a food processor and pulse until finely chopped.
Add 1 3/4 oz basil leaves, keeping a few leaves for serving, and pulse into a coarse paste.
With the motor running, pour in 1/4 cup olive oil. Add 1 oz Parmesan cheese and pulse just until combined.
Finish the dish
Bring a large pot of salted water to a boil and cook 6 oz tagliatelle until al dente, 8 to 10 minutes. Save a few tablespoons of the cooking water.
Drain the pasta and put it back in the pot. Stir in the pesto, adding a splash of the cooking water until it coats every strand.
Serve right away, with the reserved basil leaves on top.
Notes
Make the pesto up to 3 days in advance. Keep it in a jar with a thin layer of olive oil on top so it stays green. It also freezes well in an ice cube tray.