Slice the eggplant and squash lengthwise into 1/8 to 1/4-inch thick strips. Lay the strips out on baking sheet pan and salt generously. Set aside.
Slice the peppers lengthwise into 1 1/2-inch strips.
Preheat the oven to 375 degrees F.
Mix the Chavrie®, olives, thyme, and eggs together in a bowl and season, to taste, with salt and pepper.
Thoroughly wipe excess salt and moisture from eggplant and squash with paper towel.
Spread 1 cup of the tomato sauce into the bottom of an 8x11-inch baking dish. Begin layering, remembering to season with pepper between each layer. Start with the eggplant and then summer squash , peppers and pasta.
Spread sauce evenly over pasta.
Dollop spoonfuls of the cheese mixture over the sauce cover.
Repeat with the remaining eggplant, squash, goat cheese, and sauce.
Sprinkle top layer with Parmesan and bake, covered, for 30 minutes, then uncover. Continue baking until the vegetables are tender and the sauce thickens, about 15 minutes more.