Preheat oven to 350°F. Line an 8x8 inch baking pan with parchment (or spray with non-stick cooking spray). Set aside.
Heat water or milk to steaming and steep tea bags in it for about 5 minutes. When finished steeping, squeeze out the tea bags carefully with the back of a spoon to get maximum flavor from each bag. Set aside.
In a medium bowl, whisk together flour, sugar, baking powder, baking soda and salt.
In a small bowl, beat together eggs, vanilla extract, pumpkin puree, vegetable oil and steeped tea until thoroughly combined.
Add wet mixture to dry mixture and stir until just combined. (Do not over-mix.)
Pour batter into prepared baking pan. Bake for about 40 minutes or until a toothpick inserted in the center comes out clean or with a few moist crumbs. Set aside to cool completely before frosting.