In a medium Dutch oven, heat the oil and butter over medium heat. Add the potatoes, leeks and celery. Cook, stirring, until the leeks are tender, 6 to 8 minutes. Add the garlic and cook, stirring, until fragrant, about 30 seconds.

Stir in the chicken broth, thyme sprigs, salt and pepper. Bring to a simmer over medium-high heat. Reduce the heat to medium-low and cook, uncovered, until the potatoes are tender, 15 to 20 minutes.

Remove the thyme sprigs. Transfer about 4 cups of the soup to a blender. Remove the top insert from the lid and cover with a kitchen towel. Puree until smooth, 30 seconds. Add to Dutch oven with the remaining chunky soup. Stir in the cream and cook over medium-low heat, stirring, until the soup is slightly thickened, 10 to 15 minutes.

Season the soup with more salt and pepper. Garnish with celery leaves, hot sauce, prepared fried onions and another drizzle of heavy cream, if you like.