Using your food processor, combine the flour, salt and butter and pulse for about 5 seconds. Sprinkle the ice water over the flour mixture and pulse until the pastry just begins to come together, for about 10 seconds; you should still be able to see small pieces or specks of butter in it.
Transfer the pastry dough to a lightly floured work surface, gather it together to combine everything, divide the dough into 4 and shape into mounds. Wrap individually with plastic wrap and place into the refrigerator to chill for at least 30 minutes to one hour. Alternatively, you can roll out the dough immediately and place into mini tart dishes. Press down the pastry crust dough into each tart dish, on the bottom and all around the tart dish. Place into the refrigerator until ready to use.
Preheat your oven to 375 degrees.
Over medium-high heat, add the olive oil and sauté the mushrooms for about 2-3 minutes. Add the spinach and sauté for another 1-2 minutes, until the spinach is just beginning to wilt. Add the thyme leaves and season with salt, pepper and nutmeg; taste carefully for seasoning. Let cook for another 2 minutes or so and remove from the heat.
In a medium sized mixing bowl, beat the eggs and add the milk and shredded cheese. Remove the pastry crusts from the refrigerator and prick the dough a few times with a fork. You can also imprint the fork along with outer edge of the crust dough for decoration. Pour in the slightly cooled spinach and mushrooms mixture into each petite tart dish and then cover with the egg mixture until full.
Arrange the sliced mini heirloom tomatoes on top and bake at 375 degrees for about 30-40 minutes or until golden brown and cooked on top. (Check on the tomato quiche tarts after 25 minutes.) Allow to cool slightly before serving.