Preheat oven to 350 degrees Fahrenheit. Grease a loaf pan and line with parchment paper. Set aside.
In a large bowl, mix the flaxseed meal with water to make a flax egg. Let it sit for 5-10 minutes until it forms a gel-like consistency. Add the oil, sugar, apple cider vinegar, and 5 tablespoons of the milk. Then mix in the whole wheat flour and ¾ cup of the all purpose flour, along with baking powder, baking soda, and salt. It will be a thick batter.
Separate the batter into 3 bowls: 2 bowls with 1 cup each, and the third with ½ a cup. Blend the strawberries until very smooth, and add 1 cup of the puree to one of the bigger portions. Add the matcha powder to the other large third, and leave the smaller bowl plain. Add 15 tablespoons of flour to the strawberry batter, 14 tablespoons of flour to the matcha, and 7 tablespoons to the plain. Then add 14 tablespoons of milk to the matcha batter, and 7 tablespoons of milk to the plain.
Pour the batter into the prepared pan in layers: matcha first, then plain, then strawberry. Bake for about 60 minutes and let cool slightly before slicing (otherwise it could break). Enjoy!