Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, about 8 to 10 minutes. Drain and reserve about 1 cup of the pasta water.
In a blender, combine the almonds, chicken stock, olive oil, and garlic. Blend until the mixture is smooth. Pour the mixture into a large skillet and turn the heat on to medium. Bring the mixture to a boil and cook, stirring constantly, until the mixture thickens, about 3 to 4 minutes. Add the chicken, peas, cream and lemon zest. Cook, stirring frequently until the chicken is heated through, about 4 minutes (mixture will be thick). Season with salt and pepper, to taste
Put the cooked pasta into a serving bowl and add 1/2 cup of the Parmesan. Toss together until the pasta is coated. Add the chicken mixture, the remaining cheese and the basil. Toss the ingredients together, adding the reserved pasta water, as needed, to loosen the sauce. Season with salt and pepper, to taste, and serve.
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