Cut the peppers in half lengthwise; remove the core and seeds. Cook in boiling salted water 2 minutes; drain and pat dry.
Melt 1 tbsp of the butter in a medium skillet over medium heat. Add the mushrooms; sauté until golden, about 4 minutes. Remove from the heat.
Place the veal and ham in a large bowl. Mix lightly. Add the mushrooms, egg yolk, basil, parsley, wine, lemon juice, Parmesan cheese, cumin, saffron, and salt and pepper to taste. Mix well.
Fill the blanched pepper halves with the meat filling.
Melt the remaining 3 tablespoons butter in a medium saucepan over medium-low heat. Add the peppers, filled side up. Pour the chicken broth around the peppers. Sprinkle the tomatoes over and around the peppers. Heat the sauce to boiling; reduce the heat. Simmer, covered, over medium heat 20 minutes.
Transfer the peppers to a serving platter with a slotted spoon and keep warm.
Raise the heat under the saucepan and boil the liquid until slightly thickened, about 4 minutes. Pour this over the peppers and sprinkle with chopped parsley.