Thaw puff pastry according to package directions. Preheat oven to 400 degrees F. Line a baking sheet with parchment paper. Using a pizza cutter, cut pastry into six pieces (each about 5 inches long and 3 inches wide). Place pastry pieces on prepared baking sheet. Bake for 10 to 12 minutes or until golden. Using a wide metal spatula, transfer pastry pieces to a wire rack.
Meanwhile, place almonds in a large skillet; cook over medium heat about 8 minutes or until lightly browned, stirring frequently. Set aside 2 tablespoons of the almonds. In a small food processor, combine the remaining almonds, 3 tablespoons of the honey, the vanilla, and cinnamon; cover and process until ground into a thick mixture.
Gently split each slightly warm pastry piece horizontally into two layers. Carefully spoon almond mixture in small dollops on bottoms of pastry layers. Replace top layers of pastry. Using a pizza cutter, cut each pastry in half crosswise and then cut diagonally in half, to make four triangles per pastry.
Spoon the remaining 2 tablespoons honey into a glass measuring cup. Microwave on 100 percent power (high) about 10 seconds or until thinned and a pourable consistency. Drizzle the warm honey over the pastry triangles. Sprinkle with the reserved 2 tablespoons toasted almonds.