In a medium bowl, whisk together eggs, egg yolk, sugar, and brown sugar until lighter in color.

In a saucepan over medium heat, bring whipping cream, milk, and cinnamon to a simmer (do not boil).

Use a ladle to add a little of the cream to the eggs/sugar and whisk to combine. Continue adding cream while whisking until at least half has been mixed with the eggs. Add the eggs/cream mixture back to the pan and whisk to combine.

Over medium heat, cook mixture until it reaches 170 to 175 degrees F, stirring constantly.

Pour the mixture into a medium bowl. Stir in vanilla. Cover mixture directly on top with plastic wrap to prevent a skin from forming. Cool to room temperature then chill overnight.

Melt butter in a skillet over medium heat. Add pecans and cook, stirring constantly, until pecans are lightly toasted, about 2 to 3 minutes.

Transfer butter pecans to a plate to cool to room temperature.

Pour chilled mixture into an ice cream maker and freeze according to the manufacturer's instructions.

Stir in butter pecans. Transfer ice cream to a container and place it in the freezer for at least 3 hours or overnight.