Heat half of the oil in a large Dutch oven over medium heat.
Add in the chicken and season with salt and pepper. Cook undisturbed for 2-3 minutes, then stir and continue to cook for 2-3 minutes more, until nicely browned. Set aside on a plate, and cover to keep warm.
Add remaining oil to the pot and sauté the onions, celery, carrots and chopped herbs, stirring occasionally.
Once the veggies are tender, add the stock and bring to a boil, stirring all the way through the bottom of the pot to remove any brown bits. Reduce the heat and simmer for 5 minutes.
Return the chicken and stir in the fresh gnocchi. Allow the gnocchi to cook for 2-3 minutes, or until they start to float to the surface.
Meanwhile, in a small bowl whisk the flour and almond milk until smooth and fully incorporated.
Add the almond mixture together with the peas, green beans, ground parmesan to the soup; stir to combine. Simmer the soup for 10 minutes more, until hot and slightly thickened.
Season with salt and pepper to your taste.