Preheat the oven to 400°F (200°C). Line a rimmed baking sheet with aluminum foil.
Cut the spaghetti squash in half lengthwise and scoop out the seeds. Rub the cut sides with 1/2 tablespoon of the oil and sprinkle with salt.
Place the squash halves cut-side down on the prepared baking sheet and roast until a fork easily shreds the flesh, about 45–60 minutes.
While the squash roasts, heat the remaining 1/2 tablespoon oil in a large skillet over medium heat.
Season the cubed chicken with a generous pinch of salt, garlic powder, and onion powder.
Add the chicken to the hot skillet in a single layer and cook, stirring occasionally, until golden and cooked through, about 5–7 minutes (internal temperature 165°F/74°C). Transfer to a plate and set aside.
Arrange the pine nuts on a small baking sheet and toast in the oven until lightly golden, about 5–10 minutes; watch closely to avoid burning.
Place the toasted pine nuts in a food processor and pulse until crushed. Add the basil, lemon juice, minced garlic, and 1/2 teaspoon salt and process until combined.
With the processor running, stream in the 2 tablespoons olive oil until the pesto is smooth and emulsified; scrape down the sides as needed.
Use a fork to scrape the spaghetti squash flesh into strands. Divide the squash between 2 bowls and stir about half of the pesto into each bowl.
Top each bowl with the cooked chicken and additional basil if desired. Taste and season with more salt if needed, then serve.
