Preheat your oven to 400 degrees. Line a baking sheet with parchment paper or a Silpat.
Place the nuts in a food processor. Pulse until they are finely chopped.
In a medium bowl, add the chopped nuts, flour, and salt. Mix well.
In a small saucepan over medium heat, add the sugar, heavy cream, corn syrup, and butter. Stirring occasionally, cook the mixture until it comes to a rolling boil. Once boiling, continue to cook for 1 minute. Remove the saucepan from the heat and add the vanilla extract. Stir to combine.
Pour the hot mixture into the nut mixture and blend well. Set aside until cool, about 5 minutes.
Using your hands (dough will be warm), roll the dough into one-inch balls. Place the balls onto the prepared baking sheet, about 3 inches apart.
Bake 12 minutes or until thin and golden brown. Allow the cookies to cool directly on the baking sheet for about 5 minutes before transferring to a wire cooling rack.
Add chocolate chips and vegetable shortening to a microwave-safe bowl. Set the power on your microwave to 50 percent.
Heat the chocolate chips in 30 seconds intervals, for about 90 seconds. Stir in between each 30-second interval, until smooth. Drizzle the melted chocolate over the tops of the Florentine cookies when cool. Allow chocolate to harden. Enjoy!
If you notice the cookie dough becomes too firm to mold, simply soften the dough in the microwave oven at half power for 30 seconds.