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Step 1
Place ¾ cup raw cashews in a blender, preferably high-powered. Pour boiling water over to cover and let soak 30 minutes. (If you set the cashews aside and then prep and measure all of the remaining ingredients, they should be ready to go right on time!)
Step 2
Heat ¼ cup extra-virgin olive oil in a large Dutch oven or other heavy pot over medium heat. Add 1 large onion, thinly sliced, and 5 garlic cloves, coarsely chopped, season with kosher salt, and cook, stirring often, until softened and onion is translucent, 5–7 minutes. Add ½ tsp. crushed red pepper flakes and cook, stirring to release flavor, 30 seconds. Add one 4.5-oz. tube or ½ cup double-concentrated or regular tomato paste and cook, stirring often and reducing heat if needed, until it starts to stick to bottom of pot but is still bright red in color, 3–4 minutes. Add one 14.5-oz. can whole peeled tomatoes and cook, stirring occasionally and crushing tomatoes with spoon, until thickened slightly and starting to stick to bottom of pot, about 5 minutes.
Step 3
When tomato sauce is nearly done, cook 1 lb. short, chunky pasta (such as rigatoni, conchiglie, or casarecce) in a large pot of boiling salted water, stirring occasionally, until al dente. Drain pasta, reserving 1½ cups pasta cooking liquid.
Step 4
Drain cashews and return to blender. Add 1 cup fresh water and blend on high until smooth and creamy (you can’t overblend, so really go for it!). Add tomato sauce and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt and blend until smooth. Return sauce to pot and set over low heat to keep warm.
Step 5
When pasta is about 2 minutes from being done, stir ¼ cup vodka into sauce. Increase heat to medium-low and bring to a simmer; cook off alcohol, about 1 minute.
Step 6
Transfer pasta to sauce (it’s okay if some water clings to the noodles) and add ½ cup reserved pasta cooking liquid. Reduce heat to low and cook, stirring and adding more pasta cooking liquid ¼ cup at a time as needed, until pasta is coated in sauce, about 2 minutes; season with salt. (Note: This pasta stiffens as it sits. To refresh the pot for a second—or third—helping, stir in more reserved pasta cooking liquid to loosen.)
Step 7
Divide pasta among bowls and top with torn basil leaves and vegan Parmesan (if using). Season with freshly ground black pepper and drizzle more oil over. Serve with lemon wedges for squeezing over.