Put the butter into a large pot over medium heat and allow it to melt gently.
Pour in the olive oil next.
Add the sliced leeks to the pot, sprinkle with salt and pepper, and cook, stirring often, until the leeks become tender, about 6 minutes.
Mix in the minced garlic and cook for just 15 seconds to release its fragrance.
Incorporate the cubed potatoes and cook while stirring for 20 seconds.
Pour the vegetable broth into the pot and add the thyme sprigs, then bring everything up to a boil.
Cover the pot with a lid and lower the heat to maintain a soft simmer.
Let it simmer for 22 to 25 minutes until the potatoes have softened thoroughly.
Switch off the heat and fish out the thyme sprigs from the soup.
Use an immersion blender to puree the soup until it turns smooth and creamy.
Stir the heavy cream into the blended soup.
Season with salt and pepper to taste and adjust as needed.
Serve the soup in bowls and top with croutons, fresh parsley, and chopped chives.
Enjoy your delicious homemade creamy leek and potato soup.