Drain and rinse the cashews, then place in the blender with all of the other ingredients. Blend on high until creamy, smooth and emulsified, about 1 minute or so (try not to over blend as the olive oil may become bitter). Taste and add more lemon / salt / pepper if you feel it needs it. Keep the blender covered while you cook the pasta.
Cook the spaghetti in well salted boiling water until al dente, then drain, reserving about 1/2 cup of the pasta water to thin the avo sauce later. Place the spaghetti back in the cooking pot (heat turned off), and pour most of the sauce into the pot along with the halved cherry tomatoes and most of the basil. Toss together until the pasta is well coated. Now taste and add more sauce if you feel it needs it, and/or a little reserved pasta water to thin it out and keep the sauce silky.
Twirl big mounds of pasta into bowls and top with a generous sprinkling of cashew parm, the reserved basil, a few cracks of pepper, a little drizzle of quality olive oil and a tiny sprinkle of flaky sea salt. If you're feeling it, a little sprinkle of aleppo pepper flakes would not go astray! Serve with more cashew parm at the table. Eat asap.