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Preheat the oven to 325°F with a rack in the center. Line a tea loaf pan, 9" x 5" loaf pan, or 8 1/2" x 4 1/2" loaf pan with a parchment sling and lightly grease.
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Cut open all of the tea bags and empty them into a small bowl. If using tea with larger pieces, crush the tea leaves (in a mortar and pestle, or using a plastic bag and a rolling pin) to achieve a finer consistency, with no large or woody pieces remaining. Measure out 2 tablespoons (about 8g).
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In the bowl of a stand mixer or a large bowl, combine the tea, sugar, and orange oil or zest. Mix for 2 minutes on medium speed or rub the mixture between your fingers.
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Add the butter and cream cheese and beat until the mixture is homogeneous, about 1 minute on medium speed, scraping the bowl halfway through.
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Scrape down the bowl, add the milk and vanilla, and beat until thoroughly combined, about 30 seconds on low speed.
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Scrape the bowl, then add the eggs one at a time, beating to fully incorporate (about 20 seconds on medium speed) and scraping the bowl in between additions.
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In a small bowl, whisk together the flour, baking powder, and salt. Add this mixture to the wet ingredients in 2 additions, beating on low speed for about 20 seconds and scraping the bowl after each addition, until the batter has only a couple streaks of flour remaining. Use a flexible spatula to scrape the bowl and incorporate any remaining flour.
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Transfer the batter to the prepared pan and use a small offset spatula to spread it into an even layer. Rinse and dry the spatula, then use it to “draw” a line lengthwise down the center of the batter. Aim for a cut that runs nearly the entire length of the pan and about 1" deep; this will help control the rise of the loaf and give it a pretty final shape.
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Bake the cake in a tea loaf pan for 55 to 60 minutes, or until it's evenly golden brown and its top springs back when you press it with your fingertips. A toothpick or paring knife inserted into the center should come out clean or with just a few moist crumbs clinging to it. (If baking in a 9" x 5" or 8 1/2" x 4 1/2" loaf pan, bake the London fog cake for 55 to 60 minutes, until evenly golden brown, before tenting loosely with foil and baking for an additional 15 minutes.)
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Let the London fog loaf cake cool in the pan for 10 minutes before using the parchment sling to transfer it to a cooling rack. Let the cake cool completely before applying the glaze, at least 1 1/2 hours.
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To make the glaze: In a medium bowl, sift together the confectioners’ sugar and dried whole milk. Add 1 tablespoon of the milk and whisk to combine. If the mixture is dry and lumpy, add additional milk, a 1/2 teaspoon at a time, as needed until you reach a pourable consistency (similar to honey); when you drizzle the glaze into the bowl, the lines should hold for a few seconds before disappearing.
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Pour the glaze over the cooled cake and spread it all the way to the edges so it begins to drip down the sides; a small offset spatula is a helpful tool here. Set aside and allow the glaze to set before slicing and serving.
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Storage information: Leftover London fog cake can be stored at room temperature, in an airtight container, for up to 4 days. The tea flavor will strengthen as time passes.
