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1
Preheat the oven to 425.
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2
In a medium bowl, toss the flour with 1 teaspoon of the sugar and the salt.
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3
Cut in the cold butter until the mixture resembles fine crumbs.
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4
In a small bowl, beat the egg with the milk.
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5
Sprinkle 2 tablespoons of the beaten egg over the flour mixture and stir.
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6
Working quickly, gather the dough into a smooth mass, squeezing it gently.
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7
Transfer the dough to a lightly floured surface and pat it into a 5-inch disk.
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8
Wrap in wax paper and refrigerate until firm but not hard, about 30 minutes.
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9
On a lightly floured surface, roll out the dough to a 9 1/2-inch round, turning it clockwise an inch or two each time you roll to maintain an even shape.
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10
Transfer the dough to a heavy flat baking sheet.
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11
Fold up 1/4 inch of the edge of the dough to form a neat rim.
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12
Using a knife, score the rim in a decorative pattern.
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13
Brush the rim with a little of the remaining beaten egg.
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14
Brush 1 tablespoon of the apricot preserves over the bottom of the dough and refrigerate while you prepare the pears.
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15
Peel, quarter and core the pears.
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16
Slice each quarter lengthwise into 5 thin wedges.
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17
Arrange all but 6 of the pear wedges on the dough in a spoke pattern, overlapping them slightly.
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18
Cut the remaining pear wedges and arrange them in the center of the tart to form a decorative rose.
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19
Brush the pear slices with the melted butter and sprinkle with the remaining 2 teaspoons of sugar.
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20
Bake the galette in the middle of the oven for 25 to 30 minutes, or until the pears are tender and the pastry is crisp and golden.
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21
Carefully slide the galette onto a rack to cool slightly.
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22
Stir the hot water into the remaining 1 tablespoon of apricot preserves and brush on the pears.
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23
Serve the galette at room temperature.
