Place the milk, cream and 1/3 cup of the brown sugar in a small pan and cook over low heat, whisking from time to time, until it is warm, about 175 F.
Place the egg yolk, 1/3 cup of the brown sugar and salt in a small metal bowl and whisk until completely mixed. Add 1/4 cup of the warm milk mixture to the eggs, whisking all the while. Continue adding milk to the eggs, 1/4 cup at a time, until you have added about 1-1/2 cups. Slowly, whisking all the while, return the now milk and egg mixture to the remaining milk mixture in the pan and continue cooking until it just begins to thicken or reaches about 185 F. Do not allow the mixture to boil. Pour through a medium fine strainer into a metal bowl. Discard the solids. Add the pecans and stir well. Set the mixture aside until it reaches room temperature. Add the vanilla extract and stir well.
Cover and refrigerate until it reaches 40 F, about 3 hours. Transfer to an ice cream maker and proceed according to the manufacturer’s instructions.