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1
Mix cream and milk in large bowl.
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2
Whisk egg, egg yolks, and cornstarch in medium bowl.
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3
Stir sugar, 1/2 cup water, and salt in heavy large pot over medium-low heat until sugar dissolves.
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4
Increase heat to medium-high and boil without stirring until mixture turns thick, syrupy, and dark amber, occasionally swirling pot and brushing down sides with wet pastry brush, about 7 minutes.
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5
Immediately whisk in cream mixture (mixture will bubble vigorously).
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6
Stir to dissolve caramel bits.
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7
Bring mixture to boil, watching closely to prevent mixture from bubbling over, then reduce heat to medium.
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8
Gradually whisk half of hot caramel mixture into egg mixture.
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9
Return mixture to pot, whisking to blend.
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10
Whisk over medium heat until custard boils and is very thick, about 2 minutes.
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11
Remove from heat.
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12
Add butter and rum; stir until melted and smooth.
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13
Strain.
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14
Divide custard among ten 6-ounce glasses or cups.
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15
Chill uncovered until cold, about 4 hours.
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16
DO AHEAD: Can be made 1 day ahead.
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17
Cover and keep refrigerated.
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18
Place 1/2 cup cream in small saucepan.
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19
Scrape in seeds from vanilla bean; add bean.
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20
Bring to simmer over medium heat.
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21
Add butter and set aside.
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22
Stir sugar, corn syrup, and 2 tablespoons water in heavy large saucepan over medium-low heat until sugar dissolves.
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23
Increase heat to medium-high and boil without stirring until mixture turns medium amber color, occasionally swirling pan and brushing down sides with wet pastry brush, about 6 minutes.
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24
Immediately whisk in cream mixture (mixture will bubble vigorously).
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25
Stir to dissolve caramel bits.
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26
Set pan in large bowl of ice water to cool.
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27
Discard vanilla bean.
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28
DO AHEAD: Caramel sauce can be made 1 day ahead.
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29
Cover and chill.
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30
Using electric mixer, beat remaining 1/4 cup cream in medium bowl until peaks form.
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31
Add crme frache and beat until soft peaks form.
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32
Place 1 budino on each of 10 plates.
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33
Reheat caramel sauce just until warm.
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34
Spoon 1 tablespoon caramel sauce over each budino.
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35
Spoon dollop of whipped creme fraiche over and sprinkle with fleur de sel.
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36
*A type of sea salt; available at some supermarkets and at specialty foods stores.