Begin by chopping the onion, celery, and carrots into small, even pieces. Set aside.
In a large heavy-bottomed pot, melt the butter over medium heat until it begins to foam and releases a nutty aroma.
Add the chopped onion to the pot and cook, stirring occasionally, until translucent and fragrant, about 5 minutes.
Stir in the diced celery and carrots, cooking for another 5 minutes until they start to soften and release their natural sweetness.
Pour in the chicken broth, bringing the mixture to a gentle simmer. Add the shredded cooked chicken and stir to combine.
Let the soup simmer gently for 15 minutes, allowing the flavors to meld and the vegetables to become tender but not mushy.
Reduce the heat to low and stir in the cream, mixing until the soup turns velvety and smooth.
Season with salt and pepper to taste, then sprinkle with chopped fresh herbs for brightness and aroma.
Give the soup a final stir, ensuring everything is heated through and well combined. The soup should be creamy, fragrant, and inviting.
Use a ladle to serve the soup hot, garnished with additional herbs if desired, and enjoy its comforting, velvety texture.