Place a large baking sheet in the oven, then preheat the oven to 375 degrees. (Warming the baking sheet in advance helps ensure the bottom of the puff pastry cooks all the way through.)
In a small bowl, combine the ricotta and parmesan cheese with the salt and pepper. Mix well.
On a floured surface, roll one pastry sheet into a 12-15 inch circle (you will need to cut the squared off edges to make a circle - it doesn't need to be perfect because you will be rolling over the edges of the dough to form a crust).
Transfer dough to the parchment paper.
Spread the cheese mixture evenly over the dough, leaving about 2 inches all around on the outside of the circle.
Arrange the vegetables on top of the cheese mixture. (I like to work in a circle so each slice has the same amount of each vegetable, but you can get creative with your design if you like!) Press the vegetables firmly into the cheese.
Drizzle the olive oil over the vegetables and brush the crust with the whisked egg.
Slide the tart with the parchment paper onto the hot baking sheet in the oven.
Bake for 25-30 minutes or until the crust is a nice golden brown color.
Take out of oven, cut into 8 slices, then serve and enjoy!