In the work bowl of the food processor, pulse the sliced almonds until they are finely chopped, like a meal. In the 3-quart bowl, stir together the almonds, flour, orange zest, and salt.
In the small sauce pan, heat the sugar, heavy cream, corn syrup, and butter over medium heat. Stir occasionally, until the mixture boils and the sugar completely dissolves. The liquid comes to a boil rather quickly, so don’t be tempted to wander off, otherwise you could end up with burned sugar. Boil for 1 more minute, then remove from heat and stir in the vanilla. Stir the liquid into the almond flour mixture just until combined. Set aside and allow to cool until you can work with it in your hands.
While the cookie mixture is cooling, preheat the oven to 350° F.
Scoop the dough one rounded teaspoon (or rounded tablespoon) at a time and shape into balls. Place each ball on the prepared baking sheets and space them about 3 or 4 inches apart because the cookies will spread.
Bake one pan at a time, about 10 or 11 minutes, until the cookies are thin and golden brown. Rotate the pan halfway through baking. Remove from oven and cool on the baking sheet for 5 minutes, then remove to a wire rack.
You can decorate the cookies with chocolate drizzle or make sandwiches with chocolate filling. Put the chopped chocolate in a microwave-safe bowl and cook on 50% heat for 1 minute. Stir and heat again at 50% for 30 seconds. Repeat 1 or 2 more times until the chocolate is fully melted. Drizzle melted chocolate over the cookies, or put about ½ teaspoon of melted chocolate onto the flat side of a cookie and press together with another. Set the decorated cookies on a wire rack until the chocolate is set.
Store cookies in an air-tight container separated by layers of wax paper or parchment. They will store well for up to 3 days. They tend to absorb ambient moisture and lose their crispy crunch, so store them separately from moist cookies and cakes.