Preheat the oven to 350°F and line a muffin tin with 4 cupcake liners.
In a mixing bowl, whisk together the flour, sugar, matcha powder, baking powder, and salt until evenly combined.
Add the egg, melted butter, and milk to the dry ingredients. Stir until the batter is smooth and no dry streaks remain.
Divide the batter evenly among the 4 liners, filling each about two-thirds full.
Bake for 15 to 18 minutes, or until a toothpick inserted in the center comes out clean. Let the cupcakes cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.
While the cupcakes cool, place the white chocolate chips in a heatproof bowl. Heat the heavy cream in a small saucepan over medium heat until it just begins to steam, then pour it over the chips.
Let the mixture sit for 1 minute, then stir until the ganache is smooth and glossy. Spoon or spread the ganache over each cooled cupcake.