Chocolate Ice Cream

Bring milk, cream, and vanilla just to a boil in a 1 1/2- to 2-quart saucepan, then remove from heat and keep warm, covered. Place chopped chocolate in a large heatproof bowl. Stir together 1/2 cup sugar with water in a 3-quart heavy saucepan and bring to a boil over moderate heat, stirring until sugar is dissolved and washing down any sugar crystals on side of pan with a pastry brush dipped in cold water. Boil syrup, without stirring, gently swirling pan and washing down crystals, until mixture is a deep golden caramel, about 10 minutes. Remove pan from heat and carefully whisk in warm cream mixture (mixture will steam vigorously and caramel may harden). Cook over low heat, whisking, until caramel is dissolved. Beat yolks with salt and remaining 3 tablespoons sugar in a large bowl, using an electric mixer at high speed, until tripled in volume and thick enough to form a ribbon that takes 2 seconds to dissolve into mixture when beater is lifted, 3 to 4 minutes in a stand mixer or 6 to 8 with a handheld. Add hot caramel mixture to yolks in a slow stream, whisking, then transfer custard to 3-quart saucepan. Cook over moderately low heat, stirring constantly, until custard is slightly thickened and registers 170 °F on thermometer (do not let boil). Force custard through a fine-mesh sieve into bowl with chopped chocolate and let stand 1 minute, then whisk mixture until smooth. Cool to room temperature, stirring occasionally, about 35 minutes. Freeze custard in ice cream maker, then transfer to an airtight container and put in freezer to harden, at least 1 hour.