Palmiers Du Basilic (Basil-Scented Savory Cookies

1
Preheat the oven to 400°.
2
In a small food processor, combine the basil and garlic cloves and process until a paste begins to form. With the motor running, add the 1/4 cup olive oil in a slow, steady stream, processing until a smooth paste forms.
3
On a lightly floured work surface, roll out the puff pastry into a 12x15 rectangle, marking the center at top and bottom, making an imaginary line. Spread the basil paste thinly over the pastry surface. Roll the 2 narrow ends of the pastry sheet inward, not too tightly, brushing with a little olive oil to help it hold together. When the rolls meet at the center, press together very lightly, then place in the freezer for 20 minutes.
4
Lightly oil a baking sheet. Remove the pastry roll from the freezer, place on a work surface, and cut crosswise into 3/8-inch pieces. Transfer each piece to the prepared baking sheet, cut side down. Sprinkle with a little sea salt and pressing very lightly to adhere the salt.
5
Bake until golden, about 15 minutes. Using a spatula, transfer the pastries to a rack and let cool completely before serving.