Wash the kale thoroughly. If it's home grown, or from anyplace other than the supermarket, inspect it for hitch-hikers - you are likely to find some. I use the sprayer in the sink, and as hot water as comes from the spigot and give it a very careful washing. The hot water will actually soften it up a bit and help preserve more of the bright green color.
Remove the center ribs from the kale. No need to chop it up - just put it all right in the food processor and give it a few pulses so that everrything else will fit in there.
Add to the kale in the processor, the basil, walnuts, garlic, salt and pepper and lemon juice.
Pulse a few times - scrape down the sides of the processor bowl.
Run the processor on high speed for a minute or so, until everything is very finely ground up.
Scrape down the sides of the bowl, add the cheese and pulse a few times to incorporate it.
Add 1/2 cup of the olive oil through the fill tube, with the processor running.
Taste the pesto - it might need more salt, and if it is terribly thick, you might want to add more oil.
Pesto is great on pasta, as a sauce on grilled meats, mixed into roasted veggies or rice - it's good on just about everything.
You can freeze it in an ice cube tray, or as I do in a muffin tin - I line each spot in the tin with a small piece of plastic wrap. That ensures the frozen pesto will come out easily, and then I wrap each cube tightly which prevents freezer burn - store in a ziplock or other freezer safe container. To use, take out a bit ahead and allow it to thaw, then use just as you would fresh.
It will keep in the fridge for a week.
Notes
*May use parmesan cheese if you prefer. Pesto is easily made vegan by simply leaving out the cheese, or by substituting nutritional yeast in an equal amount.