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Preheat your oven to 375°F (190°C). Grease a 10 x 15-inch baking pan and set it aside.
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In a large saucepan, combine the butter and water. Bring the mixture to a gentle boil over medium heat.
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Remove the saucepan from the heat and stir in the flour, sugar, eggs, sour cream, lemon extract, lemon zest, baking soda, and salt. Mix until the batter is smooth and well combined. Pour the batter into the prepared baking pan and spread it evenly.
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Place the pan in the preheated oven and bake for 20 to 22 minutes, or until the cake is lightly golden and a toothpick inserted near the center comes out clean.
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Remove the cake from the oven and allow it to cool for about 15 minutes.
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While the cake is cooling, place the confectioners' sugar in a large mixing bowl.
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In a small saucepan, combine the milk, butter, and kosher salt. Heat over medium heat until the butter melts and the mixture just begins to boil.
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Carefully pour the hot mixture over the confectioners' sugar and whisk until smooth. If the glaze seems too thin, gradually whisk in additional confectioners' sugar until it reaches a spreadable consistency. Stir in the lemon extract and lemon zest.
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Pour the glaze over the still-warm cake and spread it evenly using a spatula. The warmth of the cake helps the glaze settle into a smooth, flavorful layer. Allow the cake to cool completely, about 50 minutes, before slicing and serving.