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1
In a heavy pot, bring the milk to a boil.
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2
Sprinkle in the semolina, whisking constantly over very low heat.
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3
Add the sugar, then simmer for 5 to 6 minutes, stirring from time to time.
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4
Remove from the heat and add the butter and the eggs, 1 by 1, stirring.
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5
Blend in the vanilla.
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6
The mixture will be thick but pourable, like a sauce.
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7
Preheat the oven to 375 degrees F.
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8
Butter a deep 10-inch baking pan.
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9
In the bottom of the pan, layer 8 sheets of phyllo, leaving the edges hanging over the sides of the pan.
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10
Brush each sheet generously with clarified butter.
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11
Pour the milk mixture over the phyllo layers.
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12
Cut the remaining sheets of phyllo about the size of the pan and brush each sheet with clarified butter.
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13
Place the buttered sheets on top of the filling, then brush the hanging bottom sheets with clarified butter and roll them up to seal.
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14
With a very sharp knife, score the top diagonally in 2 directions to make diamond-shaped slits on the surface.
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15
(This makes it easier to cut later, and also allows the syrup to penetrate the pie.)
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16
Sprinkle with a little water and bake about 1 hour, or until top is light brown and filling has set.
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17
The minute you start baking the pie, begin to make the syrup.
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18
Simmer the water with sugar and the 1/2 of lemon for about 1 hour.
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19
Remove the lemon half and squeeze the juice into the syrup.
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20
Discard the lemon.
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21
Pour the syrup over the pie the minute you take it out of the oven.
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22
Be careful, syrup will bubble vigorously and can burn you.
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23
Let cool, and serve, cutting pieces along the slits that you made before baking the pie.
