Preheat the oven to 425 degrees F. Bring a large pot of water to a boil.
Add the gnocchi to the boiling water and cook according to the package directions; drain, reserving ¼ cup of the cooking liquid.
Meanwhile, heat the oil in a large nonstick cast iron skillet over medium-high heat. Add the onions and garlic and cook, stirring occasionally, until soft, about 5 minutes. Add the ground chicken and cook, stirring occasionally, until the chicken is cooked through and the onions are golden brown, 10 to 12 minutes. Remove from the heat and season with salt and pepper.
Add the gnocchi, reserved cooking liquid, marinara sauce and red pepper flakes to the skillet with the chicken mixture and stir to combine. Add the parmesan and stir.
Sprinkle with the mozzarella. Bake on the top oven rack until hot and bubbling and the cheese turns golden, about 15 minutes. Remove from the oven and let sit for 5 minutes. Add more burrata on top because more is more. And season with salt and pepper as needed.
Garnish with fresh herbs and serve.