Using a food processor or high powered blender, add dates and pulse until they form a ball. Remove dates and place in a medium mixing bowl. Add pecans to the food processor and pulse just until a coarse crumb consistency. Be careful not to turn the pecans into flour or mill.
After shredding carrots, press as much liquid out as possible, paper towels work well.
Add all cake ingredients in the mixing bowl with the dates and combine using your hands or a wooden spoon. Evenly press cake dough into an 8 x 8-into a square pan. Cover and refrigerate while making the frosting.
Add all ingredients to a mixing bowl and beat until combined and smooth.