Finely chop 3/4 cup pecans (preferably with a knife)
Mash garlic to a paste with salt using a mortar and pestle (or mince and mash with a large heavy knife). Blend remaining 1/2 cup pecans, arugula, cheese, oil, pepper, and garlic paste in a food processor until smooth, about 1 minute.
Cook pasta in a 6-to8-quart pot of boiling salted water until al dente, 10 to12 minutes. Ladle out and reserve 1 & 1/2 cups cooking water. Drain pasta in a colander, then return to pot and toss with pesto, 1/2 cup cooking water, and chopped pecans, adding more cooking water as necessary if pasta seems dry.