In a bowl, separate from the stand mixer, whisk together eggs, vanilla, lemon zest and earl grey tea.
Add the butter to the bowl of a stand mixer with the paddle attachment in place. Beat the butter on medium until creamy.
With the mixer still on medium, gradually add the sugar, increase speed to medium-high and beat for about 5 minutes, until lightened in color and texture.
Gradually add the egg mixture, one tbsp at a time. Then beat for about 3-4 minutes on medium high. Scrape down the sides of the bowl with a rubber spatula.
Reduce speed to low and gradually add the flour, cornstarch and salt, in 3 additions. Increase speed to medium and beat until smooth. You can add the cornstarch and salt all at once with the first addition of the flour.
Scrape the batter into a greased 9 x 5 inch loaf pan and bake until a toothpick inserted in the center comes out clean. This may take up to 1 hr and 15 minutes. Allow cake to cool for about 15 minutes in the pan, then transfer to a wire cooling rack. Allow the cake to cool fully before adding the icing.
Icing
Whisk together powdered sugar and milk in a bowl until smooth. You can add more milk by the teaspoon if you want a thinner consistency.
Drizzle the icing onto the (cooled) cake. Allow icing to set, slice and enjoy.