Place 2 tablespoons butter in a skillet and melt over medium-high heat. Stir in the onions, garlic, and mushrooms. Cook and stir until onions are soft and mushrooms reduce, about 5 minutes. Remove from heat.
Meanwhile, place the remaining 2 tablespoons butter in a pot, and melt over medium-high heat. Stir in the flour; cook and stir until mixture turns golden brown, about 5 minutes. Gradually pour in the chicken broth, half-and-half, 1/2 teaspoon salt, and rosemary; stir to blend ingredients. Reduce heat to medium. Stir the gorgonzola cheese and mushroom mixture into the chicken broth mixture; bring soup to a simmer and cook 10 minutes, stirring frequently.
Place half of the soup into a blender. Blend until smooth, and return to the pot. Stir in the sherry, and season with salt and pepper to taste. Cook until mixture thickens, about 5 minutes more. Garnish with fresh parsley, if desired, to serve.