Heat butter in a large soup pot over medium heat until melted.
Add olive oil to the pot.
Put sliced leeks into the pot, season with salt and pepper, and cook for about 6 minutes until they soften, stirring often.
Mix in minced garlic and let it cook for 15 seconds.
Add the cubed potatoes and cook for 20 seconds, stirring to coat.
Pour in the vegetable broth, add the thyme sprigs, and bring the mixture to a boil.
Cover the pot with a lid, reduce heat to low, and let it simmer gently for 22 to 25 minutes until potatoes become very tender.
Take the pot off the heat.
Remove the thyme sprigs from the soup.
Use an immersion blender to puree the soup until it’s silky smooth.
Stir in the heavy cream to add richness.
Adjust the seasoning by tasting and adding more salt or pepper if needed.
Serve the soup by ladling it into bowls.
Top each bowl with croutons and sprinkle with fresh parsley and chives before serving.