In a saucepan, sauté the onion in the butter. Add the potato and bouillon. Season with salt and pepper. Bring to a boil and let simmer until the potato is tender (about 10 minutes).
Add the peas and bring to a boil again.
Remove from the burner and process with a hand-held blender until smooth. Adjust seasoning as needed.
Just before serving, garnish with the egg slices, shredded ham and strong cheddar. Season with pepper to taste.