Cut the green tops and stems off of leeks, then cut leeks into 1/4" rounds and submerge into a bowl of cold water. Agitate the leeks and let dirt settle to the bottom of the bowl. Lift leeks out of the water, making sure to leave dirt behind.
Place oil in a large pot and cook over medium. Add leeks, onions, and garlic. Cook approximately 8 minutes or until fragrant.
Add pumpkin. Season with salt, pepper, thyme, and cayenne. Cook for 30 - 40 minutes, stirring occasionally.
Cover vegetables with water and turn heat high. Once simmering, reduce the heat to medium-low and simmer 45 minutes to an hour.
Remove three cups of vegetables and liquid and place in blender. Blend until smooth. Add back to soup. Adjust seasoning to taste.