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Preheat oven to 350°F with rack in middle. Generously butter pan and dust with flour, knocking out excess.
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Whisk together dry ingredients: flour, baking powder, baking soda, and salt. Set aside.
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Beat together butter and sugar in an electric mixer at medium speed until pale and fluffy, about 5 minutes. Scrape seeds from vanilla beans with tip of a paring knife and add into butter mixture, reserving pods for another use, and beat until well combined, about 1 minute.
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Add eggs one at a time, beating well after each addition. Beat in lemon extract until well combined. At low speed add flour mixture and milk alternately in batches, beginning and ending with flour mixture, mixing until just combined.
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Spoon batter into pan, smoothing and spreading evenly. Gently tap pan on counter to eliminate air bubbles. Bake until the tip of a knife or skewer inserted into center of cake comes out clean, about 1 hour. Cool in pan 1 hour, then invert onto a rack and cool completely, about 1 hour more.