Preheat the oven to 350°F (175°C) and line a 15x10-inch pan with parchment paper.
Mix flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt in a bowl.
In another bowl, beat eggs and sugars until thick (3-4 minutes). Add vanilla. Gradually add flour mixture, then fold in grated carrots and walnuts.
Pour batter into the pan and spread evenly. Bake for 10-12 minutes.
Dust a towel with powdered sugar. Turn the hot cake onto the towel, peel off the parchment, and roll up with the towel. Cool completely.
Beat cream cheese, powdered sugar, butter, and vanilla until smooth.
Unroll the cake, spread the filling (save some for the frosting), then roll it up without the towel. Wrap in plastic wrap and chill for at least 1 hour.
Top with the remaining cream cheese filling and chopped walnuts. Slice and enjoy!