Weigh or measure the sugar into a small bowl and set aside. In another bowl, weigh or measure the flour, salt, baking powder, instant espresso powder and run a whisk through to blend.
Using a stand or handheld mixer, add the butter and the sugar and blend on medium speed for about 4-5 minutes. Scrape down the bowl. Turn the mixer back on to a medium-low speed. I take a small bowl and crack the 1st egg into it to make sure there are no eggshells before adding it to the butter-sugar mix. Repeat with the second egg. I scrape down the sides again before adding the vanilla extract, rum extract, and the mascarpone. Blend till all the ingredients are blended. Take the bowl off the stand mixer and, using a good spatula, fold in the flour mixture about a third at a time. Check the bottom of the bowl for any flour that was not folded in during this process. Loosely cover the bowl with plastic wrap and refrigerate for 2 hours.
Preheat your oven to 375°, and line 2 cookie sheet pans with parchment paper. I used a medium cookie scoop and got 2-¼ dozen cookies from this batch. Do not put more than 12 scoops on a pan. They do spread when they bake. Try and keep at least 2 inches apart from each scoop. Take a pecan half and push it down on the top of each cookie dough mound. Bake for 12-14 minutes. Keep a watch on them after 11 minutes; you want the edges to get a medium golden brown around the edges. Move them to a cooling rack once you take them from the oven.