aged Manchego cheese or Parmesan cheese (1/4 cup grated)
Bring the broth to a boil in a medium (3-quart) covered saucepan over high heat.
While the broth is heating, heat the oil in a large (4-quart) saucepan over medium-high heat. Meanwhile, chop the onion.
Add the onion to the saucepan and cook until softened, about 3 minutes. While the onion is cooking, mince the garlic and peel and dice the potato into 1/2-inch dice. Add the garlic to the saucepan and cook for 1 minute.
Stir in the sherry or wine, then add the potatoes, artichokes, salt, pepper and hot broth to the pot. Cover and return to a boil over high heat, then lower the heat to medium and simmer until the potatoes have softened, about 8 minutes.
Meanwhile, finely grate the cheese.
Remove the soup from the heat, stir in the milk, then puree in 3 batches in a blender, transferring the puree to the saucepan that held the broth. (Alternatively, use an immersion blender.) Heat the puree over medium heat until hot but not boiling. Add the cheese and stir until melted, 30 seconds. Season with additional salt, if desired.