Place the pecans, brown sugar, and eggnog in a baking dish. Stir to combine and coat the pecans.
Bake for 20 minutes, stirring once half way through, until brown sugar sauce is starting to crystallize and pecans are sticking to pan.
Turn out onto greased foil to cool completely. (may want to soak that pan immediately).
In the bowl of your food processor, pulse the pecans and 1/4 cup flour until they are finely ground. Add the remaining flour, baking powder, and salt. Pulse to combine and set aside.
In the bowl of your stand mixer, beat the butter with the paddle attachment for 30 seconds, until smooth.
Beat in the powdered sugar and combine, scraping down sides as needed. Add the rum and vanilla.
Gradually beat in the flour mixture until combined.
Turn the dough out onto a clean work surface and knead into a ball. Divide into 2 portions and cover with plastic wrap. Chill in fridge over night.
Let sit at room temperature for 20 minutes, until the dough is workable. Roll out on a clean work surface between two sheets of wax paper to form a disk, about 1/4" thick.
Slice into portions and place on a parchment lined baking sheet. Poke holes with a fork.
Bake for 15-18 minutes, until edges are light golden brown. Carefully remove from oven and cut along the edges again. Allow to cool.
Repeat with remaining dough.
When cooled, melt the chocolate in a small saucepan with the shortening over medium-low heat until smooth.
Dip the edges of the shortbread in and arrange on a wire rack to set. Sprinkle with fleur de sel or raw sugar if desired.