Preheat the oven to 400 degrees F.
Cut off the top leaf and and very bottom (about 1/4 inch) of the eggplant and slice the eggplant. Slices of about 1/2 inch are ideal.
Line a rimmed sheet pan with parchment paper.
Place the eggplant slices on the prepared sheet pan and sprinkle salt on top. Set aside for ten minutes.
Slice the tomatoes into rounds.
Line another sheet pan with parchment paper.
Place the tomato slices on the prepared sheet pan and lightly sprinkle salt on top. Set aside for ten minutes.
Cut the onion in half and slice into half moons.
Slice the olives in half if necessary.
Cut the mozzarella into 1/4 inch slices. Pat the slices dry with a paper towel.
After the ten minutes have elapsed, pat the eggplant pieces and the tomato slices with a paper towel to remove the excess moisture.
Lightly brush the eggplant with the olive oil. You will not need to use it all and want to avoid adding too much oil.
Lightly brush the tomato with the olive oil. Again, do not use too much oil.
Bake the eggplant and tomatoes for 10 minutes. They will not be completely cooked, but will continue cooking once the tart is assembled. Remove when ready and set aside to cool slightly.
Heat about 1 tbsp of olive oil in a skillet.
Add the onions to the skillet and cook until soft and translucent. I recommend cooking them over medium heat, stirring occasionally to avoid browning them.
While the eggplant, tomatoes, and onions are cooking, prepare the puff pastry.
Place a sheet of puff pastry on a piece of parchment lightly dusted with flour. Lightly dust a rolling pin with flour as well.
Roll the dough into a 9 x 12 inch rectangle.
Using a pizza cutter or sharp knife, score the dough about 3/4inch from the edge, all around. Be careful not to cut through the dough.
Place the puff pastry, with the parchment paper, onto a rimmed baking sheet.
Layer the cooked eggplant and tomato slices, slightly overlapping, alternating one then the other, on the puff pastry within the border you have scored.
Lightly brush the veggies with the remaining oil.
Add the onion, olives, and mozzarella over the surface of the eggplant and tomatoes.
Sprinkle the tart with salt and the herbes de Provence.
Beat together the egg and water in a cup.
Brush the uncovered edges of the puff pastry (the border you made) with the egg wash.
Bake for about 20 minutes until the edges of the tart are puffed up and golden, the cheese melted, and the veggies tender (i.e., you can easily pierce them with a fork).
Allow the tart to cool slightly, then slice it into squares with a pizza cutter.