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Preheat the oven to 350°F.
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Place the butter and sugar in a large mixing bowl. Beat together at medium speed until the mixture lightens in color and looks fluffy. Scrape the sides and bottom of the bowl.
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Add the baking powder and salt, mixing just to combine.
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With the mixer running at medium speed, add the first three eggs to the butter/sugar mixture one at a time. Wait until each egg is absorbed into the mixture before adding the next.
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Weigh out the flour, or measure it by gently spooning it into a measuring cup, sweeping off any excess with a straight edge.
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Add 2 tablespoons of the measured flour to the bowl after the third egg, and mix until combined. Add the fourth egg, mix until absorbed, then mix in another 2 tablespoons of flour. Continue in this fashion with the fifth and sixth eggs, alternating the addition of the egg with 2 tablespoons of the flour from the recipe.
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Add the vanilla (or vanilla bean paste) and almond extract to the milk.
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Add one-third of the remaining flour to the batter, beating gently to combine. Gently beat in half the milk. Mix in another third of the flour, then the remaining milk. Stir in the remaining flour. Scrape the sides and bottom of the bowl, then beat until the batter is smooth and fluffy, about 20 to 30 seconds at medium-high speed.
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Thoroughly grease a 10- to 12-cup Bundt pan, using non-stick vegetable oil spray or shortening (not butter; butter tends to increase sticking). Scoop the batter into the prepared pan, smoothing the top with a spatula.
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Bake the cake for 50 to 60 minutes, until it's starting to brown, appears set on top, and a toothpick or long skewer inserted into the center comes out clean. (If you're baking in a dark-interior pan, start checking at 45 minutes.) If the cake appears to be browning too quickly, tent it with foil for the final 15 minutes of baking.
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Remove the cake from the oven, and gently loosen its edges using a heatproof spatula. Turn the pan over onto a cooling rack. After 10 minutes, lift the pan off the cake.
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While the cake is cooling in the pan, make the glaze. Combine the sugar, water, and salt. Heat briefly, just to dissolve the sugar; a microwave works fine. Stir in the vanilla. Once you've turned the cake out of the pan onto a rack and lifted off the pan, gently brush the glaze all over the cake.
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Allow the cake to cool completely before cutting and serving.
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Store leftover cake, well wrapped, at room temperature for several days. Freeze for longer storage.