Preheat your oven to 350ºF grease and line a 9- by 5-inch standard loaf pan with non-stick cooking spray and parchment paper. Make sure you line the pan with parchment paper, I have made this and the paper didn't line the whole pan and the corners stayed in the pan when I tried to pull it out.
In a bowl, sift together the flour, baking powder, and salt. Stir in the tea leaves and set them aside.
In a separate bowl, beat the butter and sugar together until light and fluffy. This will take about 2 minutes using a stand mixer fitted with a paddle attachment. Add the eggs, one at a time, then add in the vanilla and mix well to combine.
With the mixer running on low, add in 1/3 of the flour followed by 1/2 of the earl grey infused milk and repeat until all of the flour and milk are used up. Mix just until combined.
Scrape the batter into your prepared loaf pan and bake in a preheated oven for 50 to 60 minutes or until a cake tester inserted into the center comes out clean
Allow the cake to cool slightly in the pan then turn the cake out onto a cooling rack to cool completely.