Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish with butter or non-stick spray.

In a large bowl, combine the bread cubes and white chocolate chunks. Toss gently to distribute evenly.

In a medium saucepan, heat the milk and heavy cream over medium heat until warm but not boiling. Remove from heat.

In a separate bowl, whisk together eggs, sugar, matcha powder, vanilla extract, and salt until smooth.

Slowly pour the warm milk mixture into the egg mixture, whisking constantly to prevent curdling.

Pour the custard mixture over the bread cubes. Press down gently to ensure all bread is soaked. Let sit for 15 minutes.

Transfer the mixture to the prepared baking dish. Bake for 40-45 minutes until set and golden on top.

Let cool for 10 minutes before serving. Dust with additional matcha powder if desired.