Thinly slice the zucchini and eggplant. Place on a paper towel lined baking sheet and sprinkle 1/2 tsp salt over the veggies. Let sit for about 30 minutes - this will help get the excess moisture out of them so they can roast properly in the oven.
Meanwhile, make the crust. Add the flours and salt to a food processor and pulse to combine. Add the butter and pulse again to combine - there will be little chunks in the mixture. Add the greek yogurt, and pulse to combine again. If it still seems a bit dry, add 2 TBS of COLD water to help the dough come together. Shape the dough into a round disc and wrap tightly in plastic wrap. Pop this in the fridge until you're ready for it.
Preheat the oven now, to 425 degrees.
In a small bowl, mix together the garlic, salt, pepper, ricotta cheese, fresh thyme, and lemon zest.
When the 30 minutes are up, use a dry paper towel to pat off the moisture that has seeped out of the veggies. Slice the tomato, and set aside with the other veggies.
Roll the dough out into a circle on a lightly floured surface, until it's about 12 inches across (doesn't have to be exact!) It should be about 1/4 inch thick. Transfer to a parchment paper-lined pan.
Spread about 3/4 of the ricotta mixture onto the rolled out dough, leaving an inch (or so) border around the edge. Lay the veggies on and add the cherry tomatoes on top. Sprinkle with a little parmesan cheese and the olive oil.
Fold the edges up, one section at a time. The more rustic looking the better - this won't look perfect! Beat the egg and bush over the edges of the crust. Sprinkle a little more parmesan over the entire thing.
Bake for 20-25 minutes, until it starts to brown but doesn't look done. Take it out of the oven, sprinkle a little more parmesan on and dollop the remaining ricotta cheese on. Bake for about 10 more minutes. If the crust seems to be browning too quickly, lay a piece of foil over the top of the galette in the oven to prevent the crust from burning.