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1
In a 9-inch cast-iron skillet, melt the butter and brown sugar over moderate heat, stirring to combine.
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2
Turn off the heat.
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3
Fit the apple quarters on their sides snugly in the skillet.
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4
Cook over moderately high heat until the juices are bubbling, about 5 minutes.
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5
Turn the apples with a spoon and cook for 5 minutes longer.
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6
Turn them rounded side up, reduce the heat to moderate and cook for 5 minutes, then turn them rounded side down and cook for 4 to 5 minutes longer.
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7
The apples should be soft when pressed gently but not falling apart.
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8
Remove the skillet from the heat.
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9
Process the almonds and sugar in a food processor until finely ground.
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10
Add the flour and salt and pulse to combine.
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11
Add the butter and pulse until the mixture resembles coarse meal.
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12
Add the egg and pulse briefly to incorporate.
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13
Add the water 1 teaspoon at a time and pulse until the dough can be gathered into a ball.
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14
Transfer it to a lightly floured sheet of wax paper and, with floured fingers, pat the dough into an even 9 1/2-inch round.
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15
Slide the paper with the crust onto a cookie sheet and refrigerate until firm or for up to 4 hours.
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16
Preheat the oven to 400.
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17
Let the dough stand at room temperature for about 10 minutes.
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18
Peel off the wax paper and cover the apples with the dough round.
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19
Bake for about 25 minutes, or until the pastry is golden.
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20
Let sit for 10 minutes, then invert the tart onto a large flat platter and serve it warm.
