Drain the soaked cashews and discard the soaking water. Place them in the body of a food processor with the drained tomatoes, 4 tablespoons of the lemon juice, 3 of the garlic cloves, basil leaves, smoked paprika, salt, and oil. Process until smooth, adding the plant milk little by little to help the mixture turn over, scraping down the sides of the bowl occasionally, about 5 minutes. Taste, adding more lemon or garlic to punch up the flavors as you like. (I've noticed that the garlic flavor starts out soft, but will become stronger as the mixture sits.) Use right away, or chill airtight for up to 1 week.