Grease a 15x10x1 inch jelly roll pan, line with parchment, and preheat oven to 375°F.
Beat cream cheese with ½ cup sugar until smooth, then mix in egg and milk. Spread evenly in the pan.
Chop pecans, cranberries, and candied ginger. Reserve ⅓ cup for batter and the rest for topping.
Whisk flour, baking powder, and baking soda.
Beat egg yolks and vanilla for 5 minutes until pale, then slowly add ⅓ cup sugar. Stir in mashed banana and ⅓ cup of the chopped mix-ins.
In a separate bowl, whip egg whites until soft peaks form. Gradually add ⅓ cup sugar and whip to stiff peaks.
Fold yolk mixture into whites gently, then fold in flour mixture in two parts until just combined.
Spread batter over filling in the pan and bake 15–20 minutes until light golden.
Dust a towel with powdered sugar. Cool cake 5 minutes, loosen edges, flip onto the towel, peel parchment, and roll from the short side. Let rest seam-side down for 10 minutes.
Blend cream cheese, powdered sugar, vanilla, and milk until smooth. Drizzle over cooled cake and sprinkle with reserved pecans, cranberries, and ginger.