In a medium saucepan over medium heat, melt the butter. Once melted, add the dark brown sugar and stir to coat in the butter. The mixture will look clumpy. Bring to a simmer and cook for another minute or two. Don't allow the mixture to burn. Just a quick simmer is all we need.
Add the heavy cream and milk. When you add these, the brown sugar mixture will likely harden into little pieces. Don't worry. Continue cooking the mixture until it comes to a simmer, stirring frequently. As the cream mixture warms, the hardened brown sugar pieces will melt back into a liquid. Once it comes to a simmer, turn off heat. Do not boil.
Whisk together the egg yolks and vanilla extract for about two to three minutes. Ladle in a scoop of the warm cream mixture into the yolk mixture and whisk. Repeat this step a few more times. This gently cooks the yolks, so they don't turn into scrambled eggs.
Add the yolk-cream mixture back to the remaining cream in the saucepan. Put the saucepan back on the stove on medium heat. Whisk constantly until the mixture thickens enough to coat the back of a spoon. Do not let it boil but a simmer is fine.
Once thickened, pour into a nonreactive bowl and cover with plastic wrap directly on the surface of the custard mixture to prevent a film from forming. Allow to cool and store in the refrigerator until cold, at least four hours to ensure proper churning, though I like to chill overnight to really make sure it's cold. The mixture needs to be cold in order to properly set up when churning.
Churn according to ice cream maker manufacturer's directions. Add the candied pecans (see below for directions) in the final two minutes or so of churning. After churning, store in an airtight container and freeze for several hours to harden. Enjoy!