Bring a large pot of water to a rolling boil. Salt the water. Prepare an ice bath and set aside.
Remove the Swiss chard leaves from the stems and blanch in the boiling water for about 1-2 minutes. Retrieve the Swiss chard with a strainer or tongs and transfer to the ice bath.
Drain the Swiss chard well - if you have a salad spinner, this helps. Roll the Swiss chard in a clean kitchen towel to remove any excess water, and try to dry as much as possible.
Place the blanched Swiss chard (you should have about 1 1/2 to 2 cups) in the bowl of a food processor or blender, along with the toasted walnuts, nutritional yeast, and garlic and process until smooth. With the food processor running, add the olive oil slowly, until it is well blended. Season to taste with salt and pepper.
Pour pesto over cooked spaghetti squash and serve.