Melt the butter in a small saucepan. Over low heat, cook the pecans until they are lightly browned, about 3 minutes. Place on a paper towel to drain and cool. In an 8-cup measuring cup with a spout, combine the remaining ingredients. Whisk until the sugar is dissolved. Pour the mixture into an ice cream maker and freeze according to manufacturers' instructions. Add the pecans 10 minutes into the freezing.