Melt the butter in a large pot over medium heat.
Add the leeks and garlic to the pot. Cook, stirring occasionally, about 2 minutes.
Add the vegetable broth, potato, artichokes, ½ tsp salt, and ¼ tsp pepper. Turn heat up to medium-high and bring to a boil.
Reduce heat to medium-low and simmer until potatoes are tender, about 25 minutes.
Puree the soup in a blender (in batches, only fill your blender halfway at the most each time).
Return the pureed soup to the pot. Add salt and pepper to taste and warm up over medium heat, if necessary.
