Bring a large pot of water to a rolling boil. Blanch the spinach for 30 seconds, then transfer to ice water to stop cooking.
In a small pot, heat 1 tablespoon of olive oil over medium-low heat. Sauté the diced onion for 10 to 12 minutes until soft and translucent. Add garlic and cook for 1 more minute. Season with salt and remove from heat.
Cook the tagliatelle in the boiling water until al dente, about 7 to 9 minutes. Reserve 1 cup of pasta water before draining.
Drain the blanched spinach and press gently to remove excess water. In a food processor, combine spinach, basil, parsley, pistachios, and lemon juice. Pulse until finely minced.
Add 2 tablespoons of olive oil, mascarpone, sautéed onions and garlic, and half of the grated Parmigiano-Reggiano to the food processor. Blend until smooth. Gradually add half of the reserved pasta water to achieve a silky consistency.
Transfer the sauce to a large bowl, toss with drained pasta, and add more reserved pasta water as needed to coat the pasta evenly.
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Notes
Serve garnished with remaining grated Parmigiano-Reggiano and a drizzle of olive oil. Store leftovers in an airtight container for up to 3 days.