Whisk the melted butter, brown and granulated sugars, and molasses in a large bowl. Add the freshly grated ginger and the egg and whisk in until very well incorporated.
In a separate bowl, sift the flour, cocoa, baking soda, cinnamon, ground ginger, nutmeg and salt and add these dry ingredients all at once to the molasses mixture. Using a rubber spatula, stir until evenly combined (the mixture will be quite soft). Stir in the chocolate mini morsels and finely chopped pecans. Cover and chill the dough for at least 2 hours or overnight.
Preheat the oven to 350°F and line two baking trays with parchment paper. If your parchment rolls up on you instead of laying flat, crumple it up once or twice, then flatten out. The parchment will now stay in place on the cookie sheet(s).
Portion 1 tablespoonful of cookie dough and shape into a ball. Roll in the granulated sugar to coat. Arrange the cookies on the baking trays, leaving 2 inches between them. Do not press the cookies flat. Bake for 10 to 12 minutes until they crackle and feel set at the edges when gently pressed with a spatula.
Let the cookies cool on the trays on a cooling rack for 10 minutes before lifting them from the tray to the rack to cool completely. The cookies will keep in an airtight container at room temperature for up to 3 days.