Cook spaghetti in a large pot of boiling salted water, stirring occasionally, until al dente; about 9 minutes. Drain, reserving 1 cup of pasta water.
In the body of a blender of food processor pulse almonds, parsley, scallions, oil, lemon, garlic, and asiago; blend until smooth. Season with salt and pepper.
Toss spaghetti and pesto in a large serving bowl. Add reserved pasta water by the tablespoon until saucy. Season with salt and pepper. Serve at once.
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