Melt butter in a large pot, over medium-low heat. Add onion and garlic, and stirring frequently, cook until vegetables are very soft but not browned, about 15 minutes. Slowly stir in flour, and cook 2 minutes.
Add potatoes and broth, and stir over medium high heat, until boiling. Reduce the heat and simmer until potato is tender and easily pierced with a fork, about 20 minutes.
Carefully place soup in a blender and blend until smooth. Place blended soup back in the large pot. Alternatively, soup can be blended with an immersion blender in the pot, but will probably not be as smooth with an immersion blender.
Add the half-and-half to the blended soup, and stir over medium-low heat until hot. Add white pepper and salt to taste.