In a medium non-stick saucepan, combine 2 3/4 cups of the cream with the rum and sugar. Bring to a simmer over medium heat, stirring to dissolve the sugar. Remove from the heat.
In a small bowl, dissolve the cornstarch in the remaining 1/4 cup cream. Add to the warm rum mixture and return to medium heat. Simmer, stirring, until the mixture thickens, 4 to 5 minutes. Remove from the heat and serve warm with the bread pudding.
Yield: about 3 cups