Preheat the oven to 375F. Butter and flour a 9x5 loaf pan.
In a microwave-safe mug, heat the milk until it's almost boiling. Add in the tea bags, and allow some time for them to steep.
In the bowl of a stand mixer, beat together the butter and sugar until light and fluffy.
Beat in the vanilla, then add in the eggs, one at a time. Add in the lemon zest.
In a medium bowl, whisk together the flour, salt, and baking powder.
Add in half the dry ingredients into the butter mixture, followed by the milk and tea, and finishing with the rest of the dry ingredients.
Pour the batter into the prepared loaf pan, and bake at 375F for 10 minutes, then lower the oven to 350F and bake for 45-50 minutes, until a toothpick inserted in the center comes out clean.
In a small bowl, whisk together the powdered sugar, lemon juice, and vanilla extract to make the glaze. Once the loaf is cool enough to handle, remove from the pan, and drizzle the glaze on top.