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1
Roll out pastry on floured surface to 11-inch squares.
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2
Using small plate as guide, cut four 5- to 5 1/2-inch rounds from each square.
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3
Transfer rounds to 2 heavy baking sheets.
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4
Cover; chill.
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5
(Can be made 1 day ahead.
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6
Keep chilled.)
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7
Mix sugar and 1/2 cup water in heavy medium saucepan.
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8
Scrape in seeds from vanilla beans.
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9
Stir over medium-low heat until sugar dissolves, occasionally brushing down sides of pan with wet pastry brush.
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10
Increase heat; boil until syrup is deep amber color, swirling pan occasionally, about 10 minutes.
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11
Remove from heat.
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12
Add 1 cup water (syrup will bubble vigorously), then rum.
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13
Stir over very low heat until caramel bits dissolve.
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14
Simmer 2 minutes.
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15
Cool syrup 15 minutes.
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16
Pour into blender.
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17
Add banana, ginger, and chiles de arbol; puree until sauce is smooth.
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18
Preheat oven to 350F.
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19
Place pineapple in 13x9x2-inch glass baking dish.
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20
Pour sauce over; turn pineapple to coat.
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21
Roast until tender, basting often with sauce and adding more water by tablespoonfuls if sauce becomes thick, about 1 hour 15 minutes.
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22
(Can be made 1 day ahead.
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23
Chill until cold, then cover and keep chilled.)
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24
Preheat oven to 375F.
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25
Transfer pineapple to work surface, scraping any sauce back into dish.
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26
Cut pineapple crosswise into 1/4-inch-thick rounds.
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27
Cut out core from each round.
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28
Place 1 pineapple round in center of each pastry round.
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29
Brush pineapple with sauce.
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30
Brush pastry edges with egg glaze.
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31
Bake tartlets until pastry is brown, about 25 minutes.
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32
Rewarm sauce.
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33
Top each tartlet with scoop of vanilla ice cream; drizzle with warm sauce and serve.
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34
*Available at Latin American markets and some specialty foods stores
