Place the spaghetti squash halves cut-side-up on a baking sheet and spray the tops with oil. Bake until tender and just beginning to brown on the edges, about 40 minutes. Allow the squash to cool slightly; if liquid has collected in the centers, drain it off, then scrape out the insides with a fork and separate it into spaghetti strands.
While the squash is baking, combine the kale, ¼ cup walnuts, cheese, olive oil, lemon juice, and garlic cloves in your food processor. Process until smooth. Season to taste with salt and pepper.
Toast the remaining walnuts and set aside.
Toss the spaghetti squash with the pesto in a large bowl. Divide onto 4 plates and top each with the toasted walnuts and sun-dried tomatoes.
The squash I used was 5 pounds. If you can't find one that big, you could buy two or three smaller ones, but note that they may need less time in the oven.