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Position rack in the lower third of the oven and preheat to 350 degrees F (175 degrees C).
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Butter a 9-inch round layer pan and line with a parchment circle.
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In a small saucepan, heat the milk and butter to almost boiling.
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Set aside.
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Sift together the flour, baking powder, and salt in a triple sifter.
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Set aside.
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Beat the eggs on medium-high speed in an electric mixer fitted with beaters or a whip attachment for about 2 minutes.
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Gradually add the sugar, 1 tablespoon at a time, taking about 4-5 minutes to blend it in well.
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Scrape the sides of the bowl occasionally.
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The mixture will thicken and turn light yellow in color.
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Reduce mixer speed to medium.
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Add the vanilla, then pour in the hot milk IN A STEADY STREAM, taking about 10 seconds.
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Immediately add the dry ingredients all at once, and beat just until blended, scraping the sides of the bowl as necessary.
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Increase mixer speed to medium-high and beat 10 seconds.
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The batter will be very thin.
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Remove the bowl from the mixer and quickly pour the batter into the prepared pan.
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Bake 30-35 minutes, or until the cake begins to come away from the sides of pan and is golden brown and springy to the touch.
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Set on a cake rack to cool for about 10 minutes.
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Run a thin knife around the sides of the pan to loosen.
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Invert pan onto the rack sprayed with nonstick coating and peel off the parchment paper.
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Invert again to finish cooling right-side up.
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Store the plain sponge layer under a glass dome or covered with aluminum foil at room temperature for up to 3 days.
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For longer storage, freeze.