Heat the olive oil in a large Dutch oven or pot over medium heat before adding the ground chicken. Cook the chicken on one side until golden brown, about 2-3 minutes, before breaking apart with a spatula.
Add the mirepoix, salt, and pepper. Continue cooking, stirring often, until the chicken is fully cooked and the vegetables have softened but not browned, another 6-8 minutes. Add the garlic and cook until fragrant, about a minute.
Add a little chicken broth to the pot and make sure to fully deglaze and get any browned bits off the bottom before adding the rest of the broth and beans. Bring to a boil before adding the pasta, covering, and cooking for 8 minutes.
After 8 minutes, remove the lid and reduce the heat to low. Add the peas and kale and cook until the kale wilts and the peas are warmed through, about 5 minutes.
Turn off the heat. Stir in the pesto and parmesan, salt to taste, and serve with a healthy squeeze of lemon juice and more freshly grated parmesan. A tiny drizzle of olive oil and some form of crusty bread are also highly recommended.