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1
Preheat oven to 325.
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2
In a 5-quart stand-mixer bowl, combine the yolks, sugar and vanilla, and beat with the whisk attachment on medium-high speed until the mixture is very pale and fluffy, about 6 minutes.
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3
Reduce mixer speed to low, combine the milk and oil in a cup and add to the yolk mixture in a steady stream.
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4
Mix flour, baking powder and salt together in a bowl, and gently fold into yolks just until combined.
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5
Line a greased 9-by-13-by-2-inch baking pan with greased parchment (or dust with a little flour).
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6
Pour in the batter, and bake until a toothpick comes out clean, about 20 minutes.
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7
Cool cake in the pan until just warm, run the tip of a knife around the edge, then remove cake to a platter or baking sheet.
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8
Make the meringue: Thoroughly clean and dry the mixer bowl and whisk attachment, and set up the mixer.
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9
Place the sugar in a heavy, large saucepan, then gently pour in the water.
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10
Set over high heat, and bring to a boil without stirring.
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11
If sugar splashes on the sides of the pan, clean it off with a wet pastry brush.
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12
Boil syrup to soft-ball stage (235 degrees) until it becomes visibly thicker, with slower, bigger bubbles, 5 to 7 minutes after it comes to a full boil.
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13
Remove the pan from heat, and let cool for 2 minutes.
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14
While the syrup cooks, add the egg whites, vanilla and salt to the mixer bowl and beat on low speed for 2 minutes, and then medium for another 4 to 5, or until the egg whites hold fluffy, stiff peaks.
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15
(Adjust the heat under the syrup or turn off the mixer longer than the other.)
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16
With the mixer running on medium-high, slowly pour the hot syrup into the egg whites, avoiding the whisk.
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17
The meringue will come almost to the very top of a 5-quart bowl.
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18
Continue beating the meringue after all the syrup is incorporated until it cools to just warm (test by touching the mixer bowl), 15 to 20 minutes.
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19
Spread meringue evenly over and around the sides of the cake, and top with chocolate shavings.
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20
Let rest, refrigerated, for at least 3 hours.
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21
It will be rich and gooey, but sliceable.
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22
After an overnight rest, the sampita will be fluffier and less gooey and will slice more cleanly.
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23
Serve with Turkish or other strong coffee.
