Melt butter in a large pot over medium heat. Cook and stir onions in melted butter until fragrant, about 5 minutes. Add mushrooms and cook until tender, about 5 minutes. Stir in dill, paprika, soy sauce, and chicken broth. Reduce the heat to low, cover, and simmer for 15 minutes.
Whisk milk and flour together in a small bowl; stir into soup. Add tomato and wax pepper halves. Cover and simmer, stirring occasionally, for 15 minutes. Season with salt and pepper. Stir in sour cream and continue to cook and stir until soup has thickened, 5 to 10 minutes. Remove and discard tomato and wax pepper halves before serving.