Toast the chopped pecans and peeled chestnuts in a medium saucepan over medium-low heat for about 5 minutes, stirring frequently.

Carefully add 1 ¼ cup water to the saucepan.

Add ¾ cup brown sugar and ½ cup granulated sugar, and stir until well mixed.

Increase heat to bring the mixture to a boil, then reduce heat and simmer for 10 minutes while stirring occasionally.

Remove the saucepan from heat and stir in 1 ½ teaspoons of vanilla extract.

Strain out the nuts using a fine mesh sieve and reserve them if desired.

Allow the syrup to cool at room temperature for 15 minutes, then transfer it to a sealed container.