Heat the milk and tea leaves in a small pot over medium-low for 5 minutes then pour into a bowl to cool. Remove the tea leaves before using!
In a medium bowl, sift together the flour, baking powder, salt, and corn starch. Set aside.
Preheat the oven to 350 F/177 C and prepare three 6-inch cake pans with a round of parchment on the bottom.
In a stand mixing bowl, cream the oil, butter, and sugar together on low for about 4 minutes until very light, white, and fluffy.
Slowly stream the eggs and vanilla into the mixing bowl, mixing well until fully incorporated.
Add in ⅓ of the dry ingredients and mix on low to combine.
Stream in ½ of the tea steeped milk, mixing until fully combined.
Add in ⅓ of the dry ingredients, mixing well on low to combine. Continue adding the next ½ of the milk and then the rest of the dry ingredients as before. Scrape the bowl down and mix one last time.
Evenly distribute the batter into the prepared cake pans. Use an offset or spatula to smooth the tops evenly. Bake together on the middle rack for 18-20 minutes, or until the tops spring back when touched. Allow the pans to cool on a wire rack for 20 minutes, then run an offset spatula around the edges and flip the layers out of the pans to continue cooling.