Instructions

1. To make Budino, in a medium heatproof bowl, combine egg, egg yolks and cornstarch. Whisk to combine and set aside. In a large heavy-bottomed saucepan over medium to medium-high heat, combine brown sugar, water and salt. Cook, swirling saucepan and stirring occasionally, until it becomes a thick, deep amber caramel, about 10 to 12 minutes. Mixture will bubble and reduce a bit as it cooks; this is normal. Watch carefully, adjusting heat as needed to avoid scorching. Remove from heat and immediately stir in cream and milk to stop the cooking. Whisk until smooth and place saucepan over high heat. Bring just to a boil, whisking, then reduce heat to medium and simmer for 3 minutes.
2. Slowly add 1 cup (250 ml) hot caramel to egg mixture, whisking constantly. Add 1 more cup (250 ml) to egg mixture, whisking constantly, then pour egg/caramel mixture back into remaining caramel in saucepan, whisking. Place saucepan over high heat and bring to a boil, whisking constantly. Continue cooking and whisking until custard thickens, about 4 to 5 minutes. Remove from heat and stir in butter and rum. Strain custard through a fine mesh sieve to remove any lumps and divide between eight 8 oz (250 ml) serving glasses or jars. Cover with plastic wrap and chill for at least 8 hours, or up to 3 days.
3. To make Caramel Sauce, in a medium saucepan, combine cream and vanilla over medium heat. Bring just to a simmer, then stir in butter until melted, remove from heat and set aside. In a large heavy‑bottomed saucepan, combine sugar, maple syrup and water over medium-high heat. Cook, swirling saucepan from time to time, until sugar turns a medium amber color, about 10 minutes. Mixture will bubble and reduce a bit as it cooks; this is normal. Watch carefully, stirring occasionally so it does not burn. Remove from heat and very carefully whisk cream mixture into caramel; it will steam and bubble. Whisk until smooth, then set aside. Can be made ahead. Let cool completely, transfer to a glass jar and refrigerate for up to 3 days. When ready to serve, transfer to a saucepan and gently warm over low heat.
4. To serve, spoon about 2 tbsp (30 ml) warm caramel sauce over each Budino, top with a dollop of whipped cream and serve immediately.