In a food processor, combine the butter, flour and pinch of salt. Pulse until the butter is about the size of small peas. In a small bowl, mix 1 egg with the ice water. Add to the flour-butter mixture. Pulse until the dough begins to come together, but is still somewhat loose and shaggy. Turn dough out onto lightly floured board and gather together lightly and quickly into a disk. Cover with plastic wrap and refrigerate at least 30 minutes before rolling out.
Place dough on floured surface and roll out into large circle, about 1/8-inch in thickness. Sprinkle the bottom of the dough with 1/4 cup of the Parmesan cheese. Begin to layer the tomatoes around in concentric circles inside the dough, leaving about a 2-inch margin of dough at the edges. Sprinkle the fresh goat cheese evenly over the sliced tomatoes. Sprinkle the remaining Parmesan cheese over the top of the goat cheese.
In a small bowl, whisk together the remaining egg with the 1/2 cup of half-and-half. Season with salt and pepper, about 1/2 teaspoon salt and 1/4 teaspoon pepper. Fold the edges of the dough up around the tomatoes, pinching the creases as you go, but casually. Enclose the tomatoes partway to make it leak-proof. Carefully pour the custard around and over the tomatoes and cheese. Brush the dough with the egg wash. Place in 400 degree oven and bake for 30 to 45 minutes, or until golden brown. Cut the tart into 10 wedges and sprinkle wit the julienned basil. Serve