Place ricotta in a small bowl. Taste and add enough sea salt that the ricotta tastes good. Add black pepper. Fold in one egg, mixing until combined, and set aside.
In a small bow, lightly beat the remaining egg and set aside.
On a lightly floured surface, roll the cold sheet of puff pastry into a 10 x 13-inch rectangle and cut into 6 equal rectangles. Add 2 -3 tablespoons ricotta in the center of each rectangle. Nestle 3 or 4 slices of peach into the ricotta. Fold the long sides over, and then the short sides, pressing each corner in.
Working quickly, move the tarts to the prepared baking sheet and brush the sides with the egg wash. Bake 17 - 20 minutes, or until the edges of the pastry and a rich golden hue and the peaches have released some of their juices.
Cool briefly, drizzle with basil oil, add flaky sea salt and black pepper, and serve.