Cook potatoes in boiling water until tender, about 15 minutes. Drain and reserve.
In a skillet, saute onion, green and red pepper in butter for 10 minutes, or until softened. Stir in the ham, green chilies, white pepper and cayenne. Cook for 1 minute longer. Reserve.
In a blender, combine the potatoes and chicken broth and blend until smooth. Add to the sauteed vegetable mixture.
Heat soup just to boiling. Beat the egg yolk with the heavy cream in a small bowl. Stir in 1/2 cup hot soup, stir yolk mixture back into sauce pan. Gently heat soup, but do not boil. Garnish with shredded cheddar cheese.
