I poached the eggs in the same water I was cooking the pasta and broccoli in.
I did them in silicone muffin liners.
I also added some sunflower seeds and garlic granules at the end when I stirred in the pesto and parmesan, except I used Grana Padano instead of parmesan, same type but cheaper.
It would be quite nice with some crispy bacon bits or chicken chunks as well.