For Potatoes: Place potatoes in a large pot and cover with cold water. Bring to a boil over high heat. Reduce to a simmer and cook until fork tender, about 10 to 15 minutes. Drain potatoes and put them into a large mixing bowl. With a handheld mixer on low speed, break up potatoes. Add the goat cheese, butter, and 1/2 cup of evaporated milk and whip potatoes on medium speed. Add additional milk until desired consistency is reached. Season with salt and white pepper to taste.
For Gravy: In a medium saucepan over high heat, bring the beef broth, Worcestershire sauce, and coffee to a boil. Reduce to a simmer. In a small bowl, dissolve the cornstarch in the water and add to broth mixture. Cook until the gravy has thickened to the consistency of cream. Whisk in butter 1 chunk at a time. Season with salt and pepper to taste.