Preheat the oven to 350F. Grease a standard 12-cup muffin tin with butter or non-stick cooking spray. Set aside.
Prepare the almond cake batter. In a medium bowl, sift together the all-purpose flour, baking powder, and salt. Set aside.
In a separate large bowl, whisk together the sugar, milk, olive oil, eggs, and both extracts until well combined.
Add the dry ingredients to the wet, and gently mix to combine.
Scoop and divide the batter evenly among the muffin wells, filling each ~⅔ full.
Bake at 350F for 15-20 minutes or until a toothpick inserted in the middle comes out clean.
While the mini cakes are baking, make the warm butter soak. In a medium saucepan over medium heat, combine the sugar, butter, water, and both extracts. Stir until the sugar is dissolved and the mixture is warm. Remove from heat.
Remove the mini cakes from the oven and let cool in the pan for 5-10 minutes.
Then using a toothpick or fork, poke holes all over the cakes that are still warm in the pan. Pour/spoon ~⅔ of the sauce over the cakes. Allow to soak for 5 minutes.
Carefully remove and invert each cake onto a serving plate.
Serve warm with a drizzle of the remaining warm butter sauce. Then top with a scoop of vanilla ice cream, followed by a drizzle of olive oil and sprinkle of flaky sea salt.
