Dice onion, leek, carrots, and celery. (Use only the white parts of the leek, discard the green stalks.)
In a large Dutch oven, add oil and preheat over medium heat.
Add onion, leeks, carrots, and celery to the pot and saute until vegetables are softened.
Smash and mince the garlic and add it to the pot. Stir and cook until garlic is fragrant.
Pour in the stock.
Add chicken meat and raise the heat to bring stock to boil. Once it starts to boil, lower the heat to medium-low, cover loosely with a lid, and let the soup cook until chicken is tender.
Take chicken out into a separate bowl and shred it using 2 forks. Add shredded chicken back to the pot.
Stir in red pepper flakes, thyme, rosemary, salt, and pepper. Taste to make sure there is enough salt.
Raise the heat again to medium-high and bring everything to a low boil.
Add gnocchi and cook until gnocchi is done and float to the top. (Gnocchi is usually ready in about 5 minutes but if using frozen gnocchi, it might take a couple extra minutes.)
Stir in fresh squeezed lemon juice and serve right away.
If you're making soup ahead of time or not planning on serving the whole batch, don't add all the gnocchi. Cook gnocchi separately and add to individual servings. Gnocchi doesn't hold up too well to being stored in liquid. It's best to cook enough gnocchi for what you need.
Soup without gnocchi is best to store in the refrigerator, in a air-tight container.
This soup will freeze very well but again, without gnocchi. Freeze soup in an air-tight freezer container and don't fill the container all the way so there is room for soup to expand as it freezes. You can also freeze it in zip-lock freezer bags.Cook gnocchi in thawed soup while reheating or cook them separately and add to individual servings of soup.