Melt the butter in a medium saucepan over medium heat. Swirl it around until fully melted, then watch closely. The butter will foam, then turn a few shades darker and develop a nutty scent. As soon as that happens, remove it from the heat and pour into a bowl to cool, scraping in all of the toasted brown bits.

In a separate saucepan, heat the milk with the rosemary sprig until it comes to a simmer. Remove from the heat and let the rosemary steep for about 20 minutes. While the milk is still warm but not too hot, discard the rosemary and whisk in the brown sugar until dissolved.

When the butter has mostly cooled, whisk in the egg yolks until well combined. An immersion blender works well for this step, but a whisk and some effort will also do the job. Pour the egg mixture into the pan with the milk and sugar. Set over medium-low heat and stir constantly with a whisk or rubber spatula, scraping the bottom and edges, until the mixture thickens enough to coat the back of a spoon. Remove from the heat and strain through a fine mesh sieve to remove any lumps.

Whisk in the heavy cream and vanilla extract. Cover and refrigerate until very cold, several hours or overnight. To speed up the process, place the mixture in the freezer, stirring every 15 minutes, until chilled.

Once cold, pour the base into an ice cream maker and churn according to the manufacturer’s instructions. While it’s mixing, combine the chopped rosemary, flaky sea salt, and toasted pecans in a small bowl. A minute or two before the ice cream is finished, add the pecan mixture and churn just until evenly distributed.

Transfer the ice cream to a container, cover, and freeze until firm. Scoop, serve, and enjoy.