Bake the biscuits: Heat the oven to 400°F and set a rack in the middle position. Line a small sheet pan or baking sheet with parchment paper if you want easier cleanup.

Open the can of biscuit dough and separate the biscuits. Put them on the prepared sheet pan, leaving a little space between each one.

Bake the biscuits until they are puffed and deep golden brown, 12 to 15 minutes. Set the pan aside when they are done.

Start the soup: Set a large Dutch oven or soup pot over medium heat. Add the butter and let it melt.

Add the chopped onion to the pot. Cook, stirring often, until it starts to soften and smell sweet, about 3 minutes.

Add the diced carrots and celery to the pot. Cook, stirring every minute or so, until the vegetables look glossy and begin to soften, 6 to 8 minutes.

Sprinkle the flour, dried thyme, 1 teaspoon salt, and 1/2 teaspoon black pepper over the vegetables in the pot. Stir well so the flour coats the vegetables and no dry patches remain.

Cook the flour mixture for 1 minute, stirring the whole time. This keeps the soup from tasting raw and pasty later.

Pour 1 cup of the chicken broth into the pot slowly while stirring. Keep stirring until the flour dissolves and you have a smooth, thick base.

Pour the remaining 5 cups of chicken broth into the pot and stir again. Increase the heat to medium-high and bring the soup to a gentle boil.

Lower the heat to medium-low so the soup bubbles softly. Simmer until the carrots are tender when pierced with a spoon or fork, about 10 minutes.

Finish and serve: Add the rotisserie chicken to the pot and stir to spread it through the soup. Let it heat for 2 minutes.