Put a large pot of water on to boil.
Pull the kale from the stems, and roughly chop. You should have about 8 cups of kale at this point.
While you are waiting for the water to boil you can toast the walnuts in a dry skillet over medium heat. Toss them frequently, and remove from the heat once they are beginning to smell fragrant and look slightly brown. Be very careful not to burn them.
When the water is boiling vigorously, add the kale. Stir so that it all submerges, and boil for about 2 minutes.
Remove the kale from the pot into a colander, and immediately rinse with cold water to stop the cooking. The kale should be bright green and quite cool.
Squeeze as much water as you can from the kale. This can be done all at once in a clean kitchen towel, or in small batches with your hands.
Place the kale, Parmesan, 3/4 cup of olive oil, toasted walnuts, garlic cloves, lemon juice, and salt in the bowl of a food processor. Pulse a few times, then run the processor until you've got a smooth paste. You will need to stop and scrape down the sides a few times.
If the pesto is a bit too chunky for you, you may choose to add the remaining 1/4 cup of olive oil.
Pesto will last about 3 days in the fridge, and freezes well either in ice cube trays, or in a flat layer in a freezer bag - you can easily break off a chunk later.