Preheat oven to 400℉ and line a cookie sheet with parchment paper or non-stick foil.
Peel the pattypan squash and remove the seeds and stems. Cut the squash into pieces roughly 1-2" in size. Depending on the size of the squash, it typically takes 2 or 3 pattypan squash to get 15 ounces of just the fleshy part of the squash.
Scatter squash pieces on the cookie sheet and roast until easily pierced with a fork, roughly 20 minutes depending on squash pieces size and ripeness of squash.
While squash cooks, cook pasta on the stove top, tear off oregano and parsley leaves from the stems, and chop arugula.
When squash is finished and still hot, place it in a food processor with the rest of the sauce ingredients and blend until smooth.
Warm up chicken in the microwave.
Place the arugula in a large bowl and cover with the hot pasta, parmesan cheese, warmed chicken and pasta sauce. Toss to mix and cover bowl with foil to trap heat so arugula softens and cheese melts. Let ingredients rest in the bowl covered for a few minutes.
Chop the chives.
Split the mixture between two bowls and top each with 1 tbsp of chopped chives and 1/8 tsp of red pepper flakes.