Place potatoes in a bowl of cold water and set aside.
Heat a large skillet over medium-high heat. Cook and stir chorizo in the hot skillet until browned and crumbly, 5 to 7 minutes.
Heat olive oil in a heavy pot over medium-low heat. Add celery and onion and cook until soft, 7 to 10 minutes.
Drain potatoes and transfer to the pot. Pour in chicken broth; add chorizo, carrots, and celery salt. Season with salt and pepper. Simmer until carrots are tender, 25 to 30 minutes.
Reserve 1/2 cup heavy cream; pour 1 1/2 cups into the soup. Continue cooking until flavors combine, about 10 minutes. Warm reserved cream slightly and whisk in flour; slowly pour into the soup. Simmer until thickened, 7 to 10 minutes more.