In a medium saucepan over medium heat, combine the cream, milk, and brown sugar. Cook, stirring frequently, until the liquid is hot and the sugar has dissolved. It should have small bubbles around the edges and steam when you stir it, but it should not come to a simmer or a boil.
Meanwhile, whisk the egg yolks for 1 minute in a medium bowl until they lighten in color. Gradually add ½ to 1 cup of the hot liquid to the egg yolks while whisking. This process is known as "tempering" the eggs which helps them come up to temperature without shocking and scrambling them by adding them directly to the hot liquid. Add the tempered egg yolks into the saucepan with the rest of the hot liquid.
Continue to cook and stir until the mixture reaches 170 degrees F on a candy thermometer or is thick enough to coat the back of a spoon and leave a clean streak where you run your finger along it. Set the pan over an ice water bath to cool it quickly, then transfer to the fridge to chill thoroughly before churning it in an ice cream maker.
In a nonstick skillet over medium heat, melt the butter. Add the chopped pecans and stir for 3-5 minutes until the nuts are toasted and the butter has browned. Watch the nuts carefully so they don't burn. Remove from the heat and set them aside to cool completely.
Once the ice cream base is thoroughly chilled, pour it into the frozen base of an ice cream maker and churn for 20-30 minutes until it reaches the consistency of soft serve ice cream. As it churns, the volume will increase because of air being added to the ice cream.
During the last 2-3 minutes of churning the ice cream, add the cooled pecans and any browned butter from the skillet to the ice cream machine. Once they are mixed in, transfer the ice cream to a freezer-safe container like a bread pan and freeze for at least 4 hours until firm and scoopable.