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1
Heat the oven to 350 degrees F. Generously butter a 8 or 9 inch cake pan that is at least 2 inches deep, and line the bottom with parchment paper.
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2
In a medium bowl, whisk together the flour, sugar, salt, baking soda, and baking powder. In a large bowl, whisk together the olive oils, milk, eggs, lemon zest, lemon juice, and St Germain. Add the dry ingredients to the wet ingredients, and whisk until just combined. The batter will be quite loose.
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3
Pour the batter into the cake pan and bake for 1 hour. The top will be golden and a cake tester inserted in the middle of the cake will come out clean. Let the cake cool for 30 minutes in the pan.
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4
Run a knife around the edge of the pan to loosen the sides of the cake. Invert the cake onto a cooling rack and let cool completely, about 2 hours.
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5
Bring milk to just under a simmer in a small saucepan over medium heat. Remove from heat and stir in dried lavender. Let sit until cool, about 10-20 minutes.
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6
Strain infused milk through a fine wire-mesh strainer and set aside 2 tablespoons for the glaze.
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7
Whisk together the infused milk, powdered sugar, salt, and lemon juice. For a thicker glaze, use less lemon juice.
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8
When olive oil cake is totally cooled, pour the glaze over the top.
