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1
In a 4 to 6 quart heavy pot, bring the milk to a boil, and reduce heat to low.
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2
Sprinkle in the semolina, whisking constantly.
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3
Add the sugar, and simmer for 5 to 6 minutes, stirring occasionally.
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4
Remove from the heat, whisk in 2/3 cup of the butter, and add eggs one at a time, stirring well after each addition.
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5
Blend in the vanilla.
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6
The mixture will be thick but pourable, like a soft polenta.
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7
Preheat the oven to 375 degrees F.
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8
Butter a 9-by-13-inch baking pan.
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9
Line bottom with 8 sheets of phyllo, layering them one at a time, and brushing each sheet with butter.
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10
The sheets will be larger than the baking pan.
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11
Be certain that the bottom is covered by pressing the dough into the corners, and allow the excess to run up the sides of the pan.
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12
Phyllo sheets not in use should always be covered with a damp towel.
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13
Pour the milk filling over the sheets.
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14
Cover with remaining 12 sheets of phyllo, repeating the layering process, and brushing each sheet with butter.
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15
With a very sharp knife, trim the dough around the edges of the pan, and score the top diagonally in two directions to make diamond-shaped slits on the surface.
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16
Sprinkle the top with a little water, and bake 45 minutes to 1 hour.
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17
Check after 45 minutes, pie is done when top is light brown and the filling is set.
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18
As soon as the pie is in the oven, begin to make the syrup.
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19
Combine water and sugar in a 4 quart sauce pan.
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20
Squeeze the halved lemon in the sugared water, and drop the juiced half in the liquid.
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21
Simmer on low heat for about 45 minutes.
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22
Discard the lemon.
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23
Very carefully, because syrup can boil vigorously, pour the hot syrup over the pie as soon as it is removed from the oven.
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24
Let the pie cool completely and then serve by cutting along the diagonal scores made prior to baking.
