In a small pot or pan over the lowest heat of the smallest burner, add milk and the teabags. Keep it over the burner for 10 minutes, or until the milk has turned a light chocolate color. Stir every so often. Remove from heat and allow to cool with teabags still in the milk.
Meanwhile, preheat oven to 350°F.
In a medium bowl, whisk together flour, ¼ cup breadcrumbs, and baking powder. Set aside.
In the bowl of a stand mixer with whisk attachment (or using a hand mixer), add eggs and salt. Beat on medium-high speed for 2 minutes.
Add in sugar, honey, and sour cream and whisk again on medium-high for another 2 minutes.
Switch to paddle attachment. Stir in dry ingredients just until combined.
Grab the milk with the teabags. Squeeze excess liquid from teabags into milk and discard bags.
Add olive oil to the milk and give it a stir.
Pour milk mixture into batter and stir just until combined.
Grease cake pan and dust bottom and sides with the remaining 2 tablespoons breadcrumbs. Pour in cake batter and bake for 40 minutes, or until a toothpick inserted comes out clean.