Begin by preheating the oven and keeping it at 350 degrees.
Grease a baking tray that measures 9 inches by 12 inches.
Break eggs into pieces and separate their yolks and egg whites.
Add vanilla, eggnog, brown sugar, and rum. Whisk them all together until they are well mixed.
Sift the nutmeg, salt, and matcha powder separately.
Mix dry and wet ingredients thoroughly.
Dip the crusty breads into the egg mixture and coat them with a good coating.
Put them on the baking tray you place aside after greasing.
Bake them for about 45 minutes. It can take between 40 and 45 minutes for them to become golden.
Cool them before serving. While cooling, dust them with powdered sugar. Then drizzle with melted white chocolate on top, and add a whipped cream dollop.