For the zucchini quinoa cakes: In a small saucepot, bring 1/2 cup water to a boil. Add the quinoa and reduce the heat to a simmer. Cover and cook until all the water is absorbed and the quinoa is cooked, 10 to 12 minutes. Spread onto a baking sheet to cool, about 10 minutes.
Meanwhile, grate the zucchini and squash. Transfer to a kitchen towel and squeeze out as much liquid as possible.
In a large bowl, mix together the cooled quinoa, grated zucchini and squash, chives, dill, mustard, garlic and lemon zest. Add the flour, cornstarch, salt, pepper and eggs and mix together well.
Heat the olive oil in a large cast-iron skillet until hot. Spoon nine 2 tablespoon-size scoops of the batter into the skillet and flatten slightly. Cook until golden on the bottom, 1 1/2 to 2 minutes. Flip and cook for an additional 1 1/2 to 2 minutes on the other side. Remove to a baking sheet. Repeat with the remaining batter.
For the herbed yogurt: Mix together the yogurt, dill, parsley, salt, pepper and lemon zest in a medium bowl.
Transfer the cakes to a platter, top with a dollop of the herbed yogurt and garnish with a sprig of dill.
To make the cakes in advance: Place the cakes on a baking sheet and keep warm in the oven at 170 degrees F for 20 to 30 minutes before serving.