Preheat your oven to 350°F (180°C) and line a 12-cup muffin tin with paper liners.
Cupcake: In a large bowl, whisk or sift together the flour, sugar, baking powder, baking soda, and salt.
In a small bowl, combine the matcha powder with ¼ cup of hot water, stirring until the mixture is smooth and lump-free. Set aside.
In a separate bowl, mix together the remaining ¾ cup of water, oil, vanilla extract, and the matcha paste. Create a well in the center of the dry ingredients and pour in the wet ingredients, stirring until the batter is smooth. Divide the batter evenly among the 12 muffin cups.
Cream Cheese Topping: Using a whisk or a hand mixer, beat the cream cheese on medium-low speed until smooth. Add the sugar, egg, and vanilla extract, and continue beating on medium-low speed until creamy and smooth. Be careful not to overmix. Add two tablespoons of the cream cheese filling to the center of each cupcake (an ice cream scoop works well for this).
Place the cupcakes in the preheated oven and bake for 22-25 minutes, or until the cream cheese filling has set and the cupcakes feel springy to the touch. A toothpick inserted into the cake portion of the cupcake should come out clean. Once baked, remove the cupcakes from the oven and let them cool on a wire rack.