Preheat oven to 350 degrees. Line a baking sheet with parchment paper.
In a large mixing bowl, add in brown and granulated sugar, cinnamon, and nutmeg. Stir together so the spices do not clump.
Add in the butter and mix on medium until light and fluffy.
Add in the sweet potato and mix until thoroughly incorporated.
Add in the eggs and vanilla and continue to mix on medium until combined.
In a medium bowl, sift the flour and baking powder. Pour into the wet ingredients and mix on low until completely combined. The dough will be very thick.
Using a cookie scoop, scoop out dough and place on the prepared baking sheet.
Place the pecans for garnish on a plate. Hold each dough ball and sprinkle pecans over top.
Using a floured bottom of a medicine cup or a finger or a spoon, make a print in the center of the cookie big enough to place the filling. I used the medicine cup because that's what I had handy. I just floured the bottom of it after each use so the cookie didn't stick to the cup.
In a medium bowl, add in the melted butter, vanilla, and brown sugar. Mix until combined. Add in the pecans and stir. The filling will become thick like a paste.
Place a spoonful of filling into each cookie. Be careful not to overfill the cookies otherwise the filling will bubble over.
Place in the oven and bake for 15 minutes or until done.