Place butter in a heavy-bottomed saucepan and slowly melt it over low heat. Continue to cook the butter until it’s melted, browned, and fragrant—usually about 3-5 minutes. Stir frequently to avoid burning.
Combine the milk, cream, and sugar in a saucepan. Whisk mixture together and bring to a simmer over medium heat. Whisk until the sugar is completely dissolved and simmer lightly for about 5 minutes. Turn off heat, add cornstarch, and whisk for about one minute to combine.
Combine the milk mixture and cooled brown butter in a blender or food processor. Blend at high speed for a minute until completely emulsified.
Cool the milk and butter mixture in the fridge for at least two hours.
Freeze in your ice cream maker according to instructions. Add the salt into the ice cream maker during the last few minutes of churning.
Pack into a freezer container and cover the top of the ice cream with plastic wrap or wax paper. Freeze for at least two hours before serving.