Melt unsalted butter in a medium saucepan over low heat, then stir in dark brown sugar and simmer for about 3 minutes.

Pour in 1 cup of heavy cream and bring to a gentle boil, simmer for an additional 3-4 minutes until thickened.

Remove from heat and add remaining heavy cream and whole milk. Stir in bourbon if using and heat until it reaches 165°F.

In a separate bowl, whisk together egg yolks and granulated sugar until pale yellow.

Gradually add hot liquid to egg yolk mixture, whisking constantly to temper. Pour back into the saucepan.

Return to medium heat, cooking until mixture thickens and coats the back of a spoon, reaching 165°F.

Remove from heat, stir in vanilla extract and kosher salt, and cool at room temperature before refrigerating for at least 4 hours.

Churn the mixture in an ice cream maker according to manufacturer's instructions for about 25-30 minutes.

Transfer churned ice cream to a container, smooth the top, seal, and freeze for at least 2 hours.

Scoop into bowls or cones and serve.