Put the egg yolks and ¾cup sugar in a heavy casserole. Beat with a wire whisk until pale yellow.
Combine the milk and cream in a saucepan. Bring just to the boil.
Add about ½cup of the hot mixture to the egg yolk mixture and beat rapidly. Add the remaining hot mixture, stirring rapidly. Scrape the tiny black seeds from the center of the vanilla bean into the custard. If vanilla extract is used, it will be added later. Heat slowly, stirring and scraping all around the bottom of the pan with a wooden spoon. Bring the mixture almost but not quite to the boil. The correct temperature is 180 degrees. This cooking will rid the custard of the raw taste of the yolks.
As the custard heats, combine the remaining ½cup sugar with the water. Heat slowly. Cook gently, stirring, until the sugar becomes golden brown. Continue cooking until the sugar is a dark amber. Take extreme care that the sugar does not burn; if it burns, it will be bitter.
Add about 1cup of the custard to the caramel, stirring. Return this caramel mixture to the custard, stirring.
Pour the mixture into a cold mixing bowl to prevent it from cooking further. Let stand until cool or at room temperature. If the vanilla bean is not used, add the vanilla extract at this point.
Meanwhile, put the pecans in a pan and place in the oven. Bake10 minutes, or until crisp and nicely toasted. Let cool.
Pour the custard mixture into the container of an electric or hand-cranked ice cream maker. Partly freeze according to the manufacturer’s instructions.
Add the pecans and continue freezing until the ice cream is solid.