Preheat oven. Coat a 9-inch round cake pan with nonstick baking spray, then line the bottom with parchment paper.
In a separate bowl, whisk together extra virgin olive oil, milk, eggs, lemon zest, fresh lemon juice, and vanilla extract.
To the pan, add shallot and lemon cut into rounds. Season lightly with Kosher salt, then cook until fragrant and softened. Add the smashed garlic cloves, then cook. Pour in white wine, then use a spatula to scrape any browned bits from the bottom of the pan. Cook.
Pour the dry ingredients into the wet, then whisk until just combined.
Pour the cake batter into the prepared pan, then use a spatula to smooth out the top. Bake for 1 hour, or until the cake is golden on top and a cake tester inserted into the center of the cake comes out clean.
Transfer to a wire rack and cool for 15 minutes. Run a knife around the edge of the pan, then invert the cake onto a plate, then back over onto the wire rack to cool fully, about 2 hours.
Lightly dust the cake with confectioner’s sugar, then slice and serve!