Preheat the oven to 400°F and arrange a rack in the center. Crush one package of freeze-dried strawberries until finely ground and coarsely crush the second package; set aside.

Roll each puff pastry sheet to a 9 1/2" x 9 1/2" square. Sprinkle sugar on top and pat it into the pastry. Flip the pastry over and spread half of the strawberry jam on it, followed by half of the ground strawberries.

Fold the right and left sides of the pastry towards the center, meeting in the middle. Repeat the process, then fold the right side over the left to form a log shape. Cut the log into 15 pieces, 1/2" to 3/4" wide.

Place the pieces on parchment-lined baking sheets, spacing them 2 inches apart. Bake for 14 to 16 minutes until puffed and golden, turning halfway through. Allow to cool for at least 15 minutes.

Divide the melted chocolate into two bowls. Add 1 Tbsp. of ground strawberries and 1 tsp. of oil to one bowl, mixing until smooth. Dip half of the palmiers into the strawberry chocolate and transfer to parchment to dry. Dip the remaining palmiers into plain melted chocolate and sprinkle with reserved crushed strawberries.