In a stand mixer fitted with the paddle attachment (or with a handheld mixer), cream together the butter, sugars, salt and vanilla for about 3 minutes on medium high speed, then scrape down the sides.
Add the flour and mix on low until it becomes crumbly. Scrape again to get all butter incorporated.
Add the pecans, chocolate and cherries and mix on low until evenly distributed. The dough will remain crumbly, but will be fully moistened.
Lay out a piece of plastic wrap on the counter. Form the dough into a log using clean hands (be sure to push it together really tightly), then wrap it completely in the plastic wrap. Roll it back and forth a few times and put pressure on each edge so it's in a nice cylinder.
Roll the dough up in a dish towel and place in the fridge for at least two hours to hydrate and firm up. The dish towel helps to prevent a flat or indented cookie surface.
When ready to bake, preheat the oven to 350℉/177℃ and line two cookie sheets with parchment paper.
Using a sharp knife, slice into ½" thick slices. Roll the log a quarter turn after each slice. If any pieces start to break off, press them back into the dough log and continue slicing.
Bake for 10-12 minutes until just slightly golden on the edges, switching pans at half.
Allow the cookies to cool on the pan for 5 minutes, then remove to a wire rack to finish cooling.