Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 13x9-inch baking pan.
Whisk eggs, maple syrup, sour cream, and butter together in a bowl. Whisk flour, tea, ginger, baking soda, and salt together in a large bowl; pour egg mixture into flour mixture and stir until all ingredients are moist. Spread cake mixture evenly into prepared pan.
Bake in the preheated oven until a toothpick inserted near the center comes out clean, about 45 minutes; remove pan to cool on a wire rack before cutting into squares, about 30 minutes.