Gather all ingredients and equipment needed.
Bring a large pot of water to a boil. Add a pinch of salt to the water and reduce the heat of the water to a simmer.
Add the gnocchi and allow them to gently poach in the water until they float (about 2-3 minutes).
Remove the gnocchi from the water using a slotted spoon or kitchen spider. Place the gnocchi into a bowl of cold water briefly. This will stop the cooking process. The gnocchi should be drained briefly on a paper towel, and then arranged on a lightly oiled baking sheet.
In a small frying pan or skillet, add butter, melt on low heat, and then whisk in all-purpose flour to make the roux. Turn off the heat and set aside.
In a large pot, on medium-high heat, add vegetable oil, sauté carrots for about 2-3 minutes, then add celery, and onions, and sauté for another 2-3 minutes, then add garlic and sauté for 1 minute.
Add chicken broth, boil, then bring down to a simmer, whisk in roux until broth thickens, then add heavy cream and stir.
Then add in cooked chicken, peas and fresh thyme leaves, cooked gnocchi and gently stir.
To serve, ladle chicken and dumplings into individual bowls or a large serving dish.