Fill a large pot with plenty of water. Bring to a boil over high heat. Once boiling, add salt generously.
While the water heats up, warm a few drops of olive oil in a skillet over medium heat. Sauté the crushed garlic until lightly golden and fragrant, 2-3 minutes. Remove and set aside.
In the same skillet, toast the walnuts over medium heat, stirring frequently, until fragrant and lightly golden, 2-3 minutes. Set aside.
Add the pasta to the boiling water and cook according to package instructions until al dente. Before draining, reserve about ½ cup of pasta water. Drain well.
In a food processor, pulse the arugula, toasted walnuts, sautéed garlic, and salt to taste until you get a coarse paste.
With the processor running, drizzle in the olive oil in a steady stream until the pesto is smooth and emulsified.
Transfer the pesto to a bowl, add the grated Parmesan, and stir well. Taste and adjust salt.
Toss the drained pasta with the pesto. If needed, add a splash of the reserved pasta water. Serve immediately or at room temperature.