Be sure your cashews have soaked for several hours, or ideally, overnight. The longer they soak, the creamier your cream cheese will be. After soaking, drain and rinse the cashews.
To the bowl of a food processor, add the soaked cashews, vinegar, lemon juice, salt, onion powder, garlic powder, and paprika, if using. Start to process to break up the cashews. You'll need to stop the food processor and scrape down the sides frequently to keep the mixture moving. Add the water 1 tbsp at a time until it comes together into a smooth spread. Be patient as this could take 5 to 10 minutes.
Once it's smooth, transfer to a mixing bowl and add the carrots, red pepper, green onion, parsley, and dill. Stir to combine.
Taste and adjust seasoning, adding more salt or a tiny splash of vinegar or lemon juice, if necessary.
Transfer the mixture to an airtight container and store in the fridge. It will set up and thicken slightly as it sits in the fridge and gets cold. You could eat it right away, but it's better cold.