Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
Roll the puff pastry to a 14-by-11-inch rectangle on a lightly floured work surface. Trim any rough edges. Transfer to the prepared baking sheet. With a paring knife or pizza cutter, lightly score a 1-inch border around the edges, taking care not to cut all the way through. Prick the center all over with a fork. Use the back of a paring knife to score diagonal ridges on the crust. Refrigerate while you prepare the filling and tomatoes.
Thinly slice the tomatoes (slightly less than 1/4 inch). Arrange the slices in a single layer on a double layer of paper towels and sprinkle with salt. Let drain 15 minutes.
For the filling, beat one of the eggs in a medium bowl. Add the ricotta, lemon zest, garlic and 1/4 cup of the Parmesan. Season with 1/2 teaspoon salt and several grinds of black pepper. Mix well to combine.
Beat the remaining egg and brush over the pastry. Sprinkle the remaining 1/4 cup Parmesan inside the border. Then spread the ricotta filling inside the border. Pat the tomatoes dry and arrange in one layer over the filling and season with salt and pepper.
Bake until the crust is puffed and deep golden brown and the ricotta is set under the tomatoes, about 25 minutes. Let cool on a rack at least 10 minutes.
Brush the tomatoes lightly with olive oil. Drizzle 1 tablespoon of olive oil over the entire tart, sprinkle with the mint and cut into squares.