Melt butter in small skillet over medium-low heat. Cook until butter turns dark amber, stirring occasionally, about 6 minutes (do not burn). Pour through fine strainer into small bowl. Bring cream and milk to simmer in large saucepan. Whisk egg yolks, both sugars, and salt in large bowl until thick and well blended. Add brown butter; whisk to blend. Gradually whisk hot cream mixture into yolk mixture; return to same saucepan. Stir mixture over medium-low heat until instant-read thermometer registers 178°F, about 5 minutes. Strain custard into large bowl. Set bowl over larger bowl of ice water. Stir until custard is cold. Stir in vanilla.
Process custard in ice cream maker according to manufacturer's instructions. Add peanut brittle during last 1 minute. Transfer ice cream to container; freeze. DO AHEAD: Can be prepared 2 days ahead. Keep frozen.
One reviewer says..."I've made this twice already and think it's one of the best ice cream recipes I've seen in a while. Very easy to make and freezes beautifully. The flavor is very similar to butterscotch."