In a large saucepan, whisk together the first 6 ingredients until smooth. Heat mixture over medium heat until slightly thickened, stirring constantly, 5-7 minutes.
Reduce heat to low; gradually add ½ cup cheese, stirring constantly with a figure-eight motion, until cheese is melted (cheese will separate from wine mixture). Gradually add remaining cheese, allowing cheese to melt between additions. Cook and stir until thickened and mixture is blended and smooth, 4-5 minutes.
Transfer to a fondue pot and keep warm. Serve with bread cubes, potatoes and/or pickles.
