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-bottom 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
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 instructions.
Drain the chile and add to the soft ice cream.
Transfer to a storage container and freeze until firm.