Preheat the oven to 400°F (200°C) and line a rimmed baking sheet with foil.

Slice the spaghetti squash in half lengthwise and scoop out the seeds. Rub the 1 tablespoon of olive oil over the cut sides, then season with salt and pepper.

Place the halves cut side down on the baking sheet and roast for 45 to 50 minutes, until a butter knife slides easily through the skin. Let cool for about 10 minutes, until you can handle them.

While the squash roasts, make the pesto. Toast the pine nuts in a dry skillet over medium-low heat for 3 to 5 minutes, shaking the pan often, until lightly golden. Let them cool for 10 minutes.

Add the toasted pine nuts, basil, ¼ cup parmesan, garlic, salt and red pepper flakes to a food processor and pulse until roughly chopped.

With the processor running, slowly stream in the ¼ cup olive oil until the pesto is smooth. Taste and adjust the salt or pepper flakes.

Use a fork to scrape the squash into strands and transfer them to a large bowl. If there's liquid pooling, drain the strands in a colander for a few minutes or blot with paper towels.

Add the chicken and pesto to the squash and toss until everything is evenly coated.

Spread the mixture in an 8x8-inch baking dish and top with the mozzarella and ½ cup parmesan.

Return to the oven and bake for 15 to 20 minutes, until the cheese is melted, bubbling and golden in spots. Let cool for 5 minutes before serving.