Preheat the broiler. Cut the tomatoes in 1/2 crosswise. Scoop out the centers leaving the outer thick flesh intact. Sprinkle the interior shells of the tomatoes with a couple pinches of salt and sugar, and invert them on a paper towel lined plate to drain until ready to stuff.
With the grating attachment of a food processor or on the large-holed side of a box grater, grate the zucchini, and place it in a strainer. Toss the zucchini with 1 teaspoon salt and place the strainer over a bowl to catch the juices. Allow to drain for 5 to 10 minutes.
In a large heavy skillet, saute the shallots in 2 tablespoons olive oil, until they begin to caramelize. Meanwhile squeeze the zucchini to release as much water as possible.
Turn the heat up on the shallots, add the dry zucchini to the pan, and saute the zucchini with the shallots for 5 minutes.
Add chopped parsley and thyme, and then toss the zucchini with the cheese, reserving 1/4 cup of the cheese for topping.
Stuff the tomatoes with the filling, mounding it slightly, and sprinkle with remaining cheese. Place in tomato halves in ovenproof baking dish and broil them until the tops are golden. Serve hot.