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1
Preheat oven to 300F.
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2
In a small heavy saucepan stir together rum, water, and 3/4 cup sugar and bring to a boil over moderate heat.
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3
Cook mixture, without stirring, until sugar is dissolved and begins to turn golden caramel.
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4
Immediately divide caramel among six 1-cup ramekins, tilting them to coat bottoms evenly.
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5
(If caramel begins to thicken before all ramekins are filled, reheat it over low heat until just pourable.)
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6
Let caramel cool.
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7
In a large saucepan scald milk with cream over moderate heat.
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8
In a large heat-proof bowl whisk together whole eggs, yolks, and remaining 1/2 cup plus 2 tablespoons sugar until mixture is combined well.
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9
Add scalded milk mixture in a slow stream, whisking constantly, and whisk in lime juice, zest, and rum extract.
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10
Strain mixture through a coarse sieve into a heat-proof pitcher or measuring cup (at least 6-cup capacity).
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11
Arrange ramekins in a baking pan just large enough to hold them and divide mixture evenly among them.
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12
Add enough hot water to baking pan to reach two-thirds up sides of ramekins.
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13
Carefully put a single piece of foil over all ramekins, tucking it loosely around them, and bake in middle of oven about 1 hour 10 minutes (custards should appear set when shaken).
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14
Remove ramekins carefully from baking pan and let creams cool.
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15
Chill caramel creams, covered, 6 hours or overnight.
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16
Run a thin knife around sides of caramel creams and gently shake them from side to side to loosen.
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17
Invert a dessert plate over each ramekin and invert caramel creams onto plates.
