Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13 inch baking dish.
Heat the olive oil in a large skillet over medium heat. Add the onion and garlic and cook, stirring often, until the onion is softened, about 5 minutes. Add the ground chicken and cook, stirring and breaking up the meat, until it is no longer pink, about 5 minutes.
Stir in the flour, thyme, oregano, rosemary, salt, and pepper and cook, stirring, for 1 minute. Add the chicken broth and bring to a simmer. Simmer until the liquid is reduced and the mixture is thickened, about 10 minutes.
Stir in the frozen peas and corn and remove from the heat. Spread the mixture into the prepared baking dish.
Spread the mashed potatoes over the chicken mixture. Sprinkle with the Parmesan cheese. Bake in the preheated oven until the top is golden brown, about 25 minutes.
Interesting Facts
Shepherd's Pie is traditionally made with ground lamb.
The origin of this dish dates back to the 1700s in England.