1. Preheat the oven to 325ºF (162ºC). Butter a 9-inch (23cm) springform pan and line the bottom with parchment paper.
2. Mix the milk with the vinegar or lemon juice in a small bowl or measuring cup, and let stand for 10 minutes at room temperature.
3. In the bowl of a stand mixer fitted with the whip attachment, beat the eggs, granulated sugar, and vanilla until it holds its shape when you lift the whip and the batter falls back on itself, about 5 minutes. Melt the butter in a medium saucepan. Remove from heat and set aside, but don’t let it get too cool. (You want it to be as close to tepid as possible when you fold it into the batter in step #7.)
4. Whisk the flour, baking powder, and salt together in a small bowl.
5. Using a flexible spatula, carefully fold one-third of the dry ingredients into the whipped eggs, being careful to deflate it as little as possible. Fold in half of the soured milk, then fold in another one-third of the dry ingredients.
6. Fold in the remaining milk, then the rest of the flour mixture.
7. Dribble in the tepid, but still liquid butter into the batter, carefully folding it in as you go, just until it’s incorporated. Be sure to reach the bottom of the bowl as you go, to avoid unincorporated lumps of flour. Don’t overfold – better to have a few lumps than to deflate the batter.
Transfer the batter carefully into the prepared pan and bake until it feels just set in the middle; a toothpick inserted into the center will come out clean, about 30 minutes. Remove the cake from the oven and increase the heat of the oven to 390ºF (200ºC).