Add butter, olive oil, garlic, and sliced leeks to a large skillet or pot over medium heat. Cook gently for about 4 to 5 minutes, stirring occasionally, until the leeks are soft. Do not let them brown.

Add diced potatoes and chicken broth. Increase heat and bring to a boil, then reduce heat to a gentle simmer. Cover loosely and cook for 25 to 30 minutes until the potatoes are fork tender.

In a separate bowl, combine sour cream and heavy cream. Season lightly with salt and black pepper, then stir until smooth. Set aside.

Remove the soup from heat and let it cool slightly. Working in batches, transfer the mixture to a blender, filling it no more than one-third full. Blend until completely smooth.

Transfer the blended soup to a large bowl and repeat with the remaining mixture.

Temper the cream mixture by stirring in 2 to 3 tablespoon of the warm soup. Mix well.

Add the tempered cream mixture back into the soup and stir until fully combined. Taste and adjust seasoning if needed.