Preheat Blackstone griddle to medium heat. Drizzle vegetable oil then add the chicken to one side of the griddle and the gnocchi to the other. Season the chicken with salt and pepper. Cook for 7-8 minutes until the gnocchi is seared and the chicken is fully cooked.
Add the mushrooms, garlic, and kale to the griddle. Cook for another 4 minutes until tender. Pour the chicken broth, sour cream, and lemon juice, and zest over the the gnocchi. Stir with spatulas for 1-2 minutes until the sour cream reduces and forms a sauce coating the gnocchi.
Remove the gnocchi from the griddle and set it on a large serving platter. Top with parmesan cheese and serve immediately.
