In a large pot over medium heat, melt the butter. Add the onion and cook, partially covered, for 10 minutes, or until the onion is soft. Add the chicken stock, peas, potato, and salt. Bring to a boil.

Reduce the heat, cover, and simmer for 7 to 8 minutes, or until the peas are soft. Remove from the heat.

Process the mixture in batches: Using a slotted spoon, transfer some of the peas to a blender. (The blender should be no more than one-third full.) Add enough of the liquid to cover. Process until smooth, then transfer to a large bowl. Repeat for the remaining mixture. Save a few peas for garnish. (You’ll have more broth than you need, which is fine: Just leave it in the pot.)

Return the pea mixture to the pot, add the heavy cream, and stir. Gently reheat the soup. Taste and add pepper and more salt, if desired. Serve hot, passing the cheese and peas at the table.