Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper and set aside.
Roll out the puff pastry so it's 1/2 inch bigger on all sides. Transfer to the prepared baking sheet and use a fork to prick all over the pastry, leaving a 1/2-inch border all around. Scatter the fontina all over the pastry (leaving the border untouched) and set aside.
In a large bowl, toss the tomatoes with the oil, Italian seasoning and some salt and pepper. Arrange the tomatoes in a single layer (it's ok if they overlap a little) over the crust--leaving the border--and sprinkle the Parmesan evenly over the top.
Bake until the tart is deep golden brown and crispy, about 25 minutes. Let rest for 5 minutes.
Tear the basil leaves, then sprinkle the basil over the tart before cutting it into squares.