Quarter the chile lengthwise and remove the seeds, veins, and any
remnants of stem. Chop it into 1/4-inch pieces. Place the chopped
chile in a small saucepan. Add water and 1 cup of the sugar. Bring
to a gentle boil over medium-low heat. Cook for 10 minutes, then
remove from the heat and let stand for at least 4 hours.
In a medium-size heavy-bottomed saucepan, combine milk, cream and
1 tablespoon of the sugar. Bring to a scald.
Meanwhile, put remaining sugar (1/2 cup plus 3 tablespoons), egg
yolks and framboise or vanilla extract in a large bowl and whisk
just to blend. While gently whisking the yolks, drizzle the hot
cream mixture into them so that they are gradually warmed up. Return
the mixture to the saucepan and set over medium-low heat. Cook,
stirring with a wooden spoon and constantly scraping the bottom
of the pan, until the custard has thickened slightly and coats the
back of the spoon.
Strain the custard through a fine sieve into a bowl and nestle it
in a larger bowl of ice. Let cool, stirring occasionally, then transfer
to an ice cream maker and freeze according to the manufacturer's
Drain the chile and add to the soft ice cream. Transfer to a storage
container and freeze until firm.