Melt the butter in a soup pot over medium heat, then add the olive oil.
Add the sliced leek, season with salt and pepper, and sauté for about 6 minutes until softened, stirring frequently.
Stir in the garlic and cook for 15 seconds, then stir in the cubed potatoes for 20 seconds.
Pour in the broth, add the thyme sprigs, and bring the soup to a boil.
Cover, lower the heat to a gentle simmer, and cook for 22 to 25 minutes until the potatoes are very soft.
Remove the pot from the heat and take out the thyme sprigs.
Use an immersion blender to blend the soup until smooth, then stir in the heavy cream.
Taste and adjust the salt and pepper, ladle soup into bowls, garnish with croutons, parsley, and chives, and serve.