In a medium skillet, heat the oil over medium heat. Cook the summer squash until lightly browned on both sides. Pour onto a plate and set aside.
In the same saucepan, mix together the water, quinoa and salt. Bring to a boil and reduce to low and allow to simmer for around 15 minutes.
Mix in the lemon juice, lemon zest, dill and Parmesan. Serve immediately.