After soaking your cashews, make a cashew cream. Drain the cashews and add them to a blender. Then add the non-dairy milk to the blender with a pinch of salt and pepper. Blend on high until completely smooth. It may take a few minutes, depending on your blender. Set the cashew cream aside.
Cook the pasta according to package directions, making sure to reserve some pasta water before you drain the pasta.
Heat a large skillet on medium high and add the lemon juice and lemon zest.
Add the cashew cream you made to the skillet, and whisk to combine with the lemon juice and zest
Reduce heat to medium low and simmer the sauce for 1-2 minutes it should thicken a bit.
Add the vegan butter a little at a time to the sauce, whisking until it has all melted into the sauce.
Add the vegan Parmesan to the sauce, then continue whisking until the Parmesan has melted into the sauce.
Taste and adjust seasoning, adding black pepper and salt if needed. I always add pepper, but sometimes the Parmesan is salty enough or you just need a bit of salt. It will be pretty tart, but that will work when the pasta/pasta water is added.
When the pasta is cooked and drained, add the pasta to the skillet and toss to start to coat, now add a little of the pasta water at a time until the sauce is the consistency you want.
It should be very creamy. Taste again and adjust seasonings. Serve immediately with chives if desired.
Notes
*Soak the cashews in room temperature water for at least 8 hours, or boil the cashews for about 20 minutes.