Preheat the oven to 350F / 180C.
Heat two skillets over medium flame and add 2 tablespoons of olive oil to each. In one, place the onions; in the other place the tomato slices. Season both lightly with salt. Let both cook slowly. Add the garlic to the tomatoes.
When the onions are thoroughly wilted and begin to brown, after about 20 minutes on the heat, add the petimezi or sweet wine. Cook until caramelized lightly, another 3 – 5 minutes.
Gently stir the honey into the tomatoes, too, and cook a few more minutes, until thick. Add the chopped herbs. Set aside both skillets and let cool slightly.
Whisk the feta, egg white and milk together in an electric mixer until a smooth paste forms.
Roll out the dough or puff pastry to fit inside a 10-inch / 22.5-cm tart pan. Oil the tart pan and place the pastry or dough inside, leaving at least 2 inches / 5 cm hanging over the rim.
Brush the surface of the dough with remaining olive oil, saving a little for the rim, too. Spread the feta mixture over the bottom of the pie. Season with ground black pepper. Spread the onions, then the tomato mixture on top. Turn the edges of the pastry crust inwards to form a decorative rim. Brush that with olive oil.
Bake in the lower half of the oven for about 25 – 35 minutes, until the crust is golden and the filling set. Remove, cool slightly, and serve.