Roast the spaghetti squash: preheat the oven, halve and seed the squash, rub with 1–2 Tbsp avocado oil and a pinch of sea salt, cut-side down on a baking sheet, and roast until tender; when cool, scrape out the strands into a large bowl.
Make the pesto: in a food processor add basil, pumpkin seeds, Parmesan (if using), and the garlic clove; pulse a few times to chop, then with the processor running slowly stream in 2/3 cup avocado oil until the pesto reaches your desired texture.
Heat a skillet over medium-high; add 1 Tbsp avocado oil (add a second Tbsp if needed). Add the chopped chicken, 1/4 tsp sea salt, paprika, and garlic powder.
Brown the chicken without stirring for 3 minutes, stir, then brown without touching for another 3 minutes; stir again, cover, and cook until cooked through, about 2–5 more minutes.
Toss the spaghetti squash strands with the pesto in the large bowl until evenly coated.
Add the cooked chicken, including any pan juices, to the bowl and toss everything together; taste and add additional sea salt if needed before serving.