Heat the olive oil in a large saute pan, over medium heat. Season the veal with 1/4 teaspoon salt and 1/8 teaspoon pepper. Add the veal to the pan and brown, about 5 to 6 minutes. Add the onions and saute for 2 minutes. Add the mushrooms and 1/4 teaspoon salt and 1/8 teaspoon pepper. Cook for 3 to 4 minutes, or until the mushrooms have released most of their liquid. Add the shallots and tomatoes and cook for 2 minutes. Add the 2 tablespoons of garlic and saute for 1 minute. Add the veal reduction and bring the liquid up to a boil. Reduce to a simmer and cook for 6 to 8 minutes. Adjust seasonings with salt and pepper, to taste. Stir in the butter and parsley. Set aside and keep warm.
Bring a pot of salted water to a boil. In a mixing bowl, combine the cheese, remaining teaspoon of garlic, remaining 1/4 teaspoon of salt, remaining 1/8 teaspoon pepper and basil. Mix well. Divide the cheese mixture evenly among the centers of each of 16 squares of the fresh pasta. With a little water, lightly wet the edges of the pasta. Place the remaining pasta squares over the cheese. Press the 2 squares of pasta together tightly, then crimp using the tines of a fork to seal the ravioli completely. Place the ravioli in the boiling water, in batches if necessary, and cook until tender, about 4 to 5 minutes. Remove from the water and drain completely.
To serve, place 2 ravioli in the center of each shallow bowl. Spoon the stew over the pasta. Garnish with the cheese and chives.