Preheat the oven to 350º F (180º C). Grease a 9 x 5-inch loaf pan.
On the stove or in the microwave heat the milk until near-boiling. Cut open the tea bags and add the tea to the milk. Allow cooling. Strain through a sieve, discard solids, and reserve milk.
In a large bowl, mix together flour, baking powder, baking soda, cinnamon, and salt. Set aside.
Using an electric hand mixer or a stand mixer, beat butter until creamy on medium-high speed, about 3 – 4 minutes. Add the sugar and beat on high speed for 4 minutes until creamed and pale, scraping down the sides and up the bottom of the bowl with a rubber spatula as needed. Add the banana and mix until incorporated. Then, beat in the oil and vanilla extract.
Turn the mixer to low and add the flour mixture in three batches, alternating with tea brewed milk mixture, beginning and ending with the flour mixture; beat until just combined, about 30 – 45 seconds. Do not overmix. Spread batter evenly into the prepared pan. If desired, sprinkle the top with rolled oats and turbinado sugar.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Allow cooling before cutting and serving.