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1
Combine flour, salt, and sugar in large bowl.
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2
Add butter and shortening; rub in with fingertips until mixture resembles coarse meal.
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3
Mix 3 tablespoons ice water and vinegar in small bowl.
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4
Pour over flour mixture.
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5
Stir with fork until moist clumps form, adding more water by teaspoonfuls if dough is dry.
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6
Gather dough into ball; flatten into disk.
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7
Wrap in plastic and refrigerate at least 30 minutes.
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8
Melt butter in heavy large skillet over medium-high heat.
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9
Add apples and saute until brown and almost tender, about 15 minutes.
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10
Reduce heat to medium; mix in cardamom.
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11
Pour 1/3 cup honey over and cook 1 minute.
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12
Position rack in top third of oven; preheat to 400F.
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13
Roll out dough between 2 sheets of parchment paper to 12-inch round.
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14
Remove top sheet of paper.
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15
Sprinkle crust evenly with nuts.
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16
Replace paper atop crust and roll to 13-inch round, embedding nuts in dough (crust will be thin).
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17
Invert crust onto rimless baking sheet.
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18
Remove top paper.
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19
Spoon half of apple mixture over crust, leaving 2-inch plain border.
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20
Sprinkle dates over apples.
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21
Top with remaining apple mixture.
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22
Using paper as aid, fold outer edge of crust over apples (dough is delicate; press together any tears).
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23
Whisk egg and milk in bowl.
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24
Brush edges generously with egg mixture.
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25
Sprinkle crust and apples with raw sugar.
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26
Bake tart until crust begins to brown, about 15 minutes.
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27
Reduce heat to 375F; bake until crust is golden brown, about 10 minutes longer.
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28
Loosen tart from parchment paper with spatula.
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29
Cool on baking sheet until warm, about 45 minutes.
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30
Beat cream and 2 tablespoons honey in large bowl until peaks form.
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31
Slide 9-inch-diameter removable tart pan bottom under tart and transfer to platter.
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32
Serve with honeyed whipped cream.