Preheat oven to 375 degrees. With a fork, prick potatoes all over; bake until tender, 45 minutes to 1 hour. While still piping hot, cut open potatoes and scoop out pulp into a mixing bowl. Beating vigorously with a wooden spoon add eggs, then add enough flour, a bit at a time, to make a tight but workable dough flexible enough to pipe from a pastry bag. Season to taste with salt and pepper. Transfer dough to a pastry bag fitted with a 3/4-inch tip and pipe out long cylinders onto a wax paper-lined cookie sheet. Chill until firm. Cut each cylinder into 1-inch pieces. Lightly flour work surface and roll pieces, one at a time, over prongs of a fork, or over a gnocchi dowel.

Bring a large pot of salted water to a boil.

Heat a sauté pan over low heat, add 3 tablespoons of the butter, and once melted, add the mushrooms. After 5 minutes, add garlic and tomatoes. Toss and cook for 2 minutes longer.  Add the wine.

Meanwhile boil gnocchi, testing frequently for doneness. Using a large slotted spoon or a spider, remove gnocchi to pan and toss with mushroom mixture and herbs and remaining tabelspoon of butter; season to taste with salt and pepper. Serve in warmed shallow bowls, topped with freshly-grated cheese and olive oil to taste.