Wash and pat dry the kale and fresh basil. Remove and discard the kale stems, give the kale leaves a rough chop and add them to a food processor along with the basil, garlic, sunflower seeds, and parmesan cheese.
Pulse 5 or 6 times to get everything chopped up. Turn the food processor on and slowly add the oil while the processor is processing. If you added ¼ cup of oil, you will end up with thick, spreadable pesto. You can stop here or if you desire a thinner consistency to use the pesto as pasta sauce, continue adding oil (about an additional ¼ cup) until the pesto reaches the consistency you want.
Use immediately or refrigerate for up to 1 week (you can also make the sauce in bulk and freeze it for later).
Notes
If using the pesto as pasta sauce, use about ½ cup of oil or more to get the sauce to the desired consistency. For spreadable pesto used in sandwiches or in a marinade use about ¼ cup of oil.