Preheat the oven to 350 degrees F. Grease a 6 by 3-inch springform pan with butter, line the bottom and sides with parchment paper, and grease the paper.
Add the lemon juice to the milk to sour it. Set aside for 5 to 10 minutes or until curdled.
In a small bowl, whisk the eggs together. Set aside.
In another small bowl, use your fingers to work the vanilla bean seeds into the sugar. Remove any bits of the pod that may have come off with the seeds. Set aside.
Place a large sifter or a sieve in a large mixing bowl. Add the flour, baking powder, baking soda, and salt and sift.
Using an electric mixer with beaters or a paddle attachment, beat the butter for 30 seconds on medium speed and then gradually add the sugar. Scrape down the sides of the bowl. Continue beating on medium speed for another 4 minutes or until light in color and fluffy.
Add the vanilla extract and beat until combined.
With the mixer still on medium speed, gradually add the eggs. If the batter curdles, add 1 to 2 tablespoons of the flour to bind it back together.
On low speed, add the flour mixture and then the oil and milk; mix until just combined. Don’t overbeat. Scrape down the sides and bottom of the bowl.
Pour the batter into the prepared pan and smooth the top. Bake in the center of the oven for 50 to 55 minutes. Cover the top of the cake with tinfoil after 30 minutes so the cake doesn’t take on too much color. When a wooden skewer inserted into the center comes out clean, and the cake bounces back when lightly pressed, remove the cake from the oven and let it stand for 10 minutes. Run a butter knife around the cake to gently release. Peel off the parchment paper from the sides. Invert the cake, peel off the bottom piece of parchment, and cool on a wire rack.