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Preheat oven to 350 degrees F. Lightly grease and line with parchment paper an 8-in. square pan or a 9x13-in. baking pan. (Note: Allow parchment to overhang pan for easier removal of cake.)
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In bowl, whisk together milk and apple cider vinegar; let rest 5-10 minutes.
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In large bowl, whisk together flour, sugar, baking powder and salt.
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Add lemon extract, milk-ACV mixture and oil and mix with mixer until just combined. (NOTE: If batter seems extremely thick, add extra milk, 1 Tbsp. at a time, until batter is somewhat pourable but not runny or thin.)
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Pour batter evenly into prepared pan, spreading evenly.
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Bake for 20-25 minutes, or until toothpick in center comes out clean.
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Let cake cool for 30 minutes before carefully lifting from pan and onto rack to cool completely.
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In bowl, combine cream cheese and butter with mixer on medium-high speed until smooth and pale.
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Add powdered sugar, vanilla and milk and mix on medium speed until smooth and fluffy. (Note: Add more milk, 1 Tbsp. at a time, if too thick or powdered sugar if too thin.)
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Using metal or rubber spatula, top cooled cake with frosting and spread until fully coated and smooth. Top with sliced strawberries.
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Cut into squares to serve.