Start by heating sugar in a heavy-bottomed saucepan over medium heat. Don’t stir initially; just swirl the pan occasionally as the sugar melts and turns amber. This takes patience, usually around eight to ten minutes. Watch carefully because sugar can burn quickly once it starts browning. When it reaches a deep golden color and smells nutty and sweet, remove it from heat immediately.

Carefully pour in the heavy cream while whisking constantly. The mixture will bubble dramatically, so stand back slightly. Once the bubbling subsides, add the butter and whisk until completely smooth. Return the pan to low heat if needed to dissolve any hardened sugar bits. Set this caramel mixture aside to cool slightly.

In a separate bowl, whisk together egg yolks until smooth. Heat the milk in another saucepan until it just begins to steam. Slowly pour about half the hot milk into the yolks while whisking constantly. This tempering process prevents the eggs from scrambling. Pour the yolk mixture back into the saucepan with the remaining milk.

Cook the custard over medium-low heat, stirring constantly with a wooden spoon or silicone spatula. The mixture is ready when it coats the back of the spoon and reaches about 170 degrees Fahrenheit. Remove from heat and stir in the vanilla extract and salt. Combine the custard with your cooled caramel mixture, whisking until completely incorporated.

Strain the mixture through a fine-mesh sieve into a clean bowl to remove any cooked egg bits. Cover and refrigerate for at least four hours, or preferably overnight. The colder your base, the better your ice cream will freeze. Churn in your ice cream maker according to manufacturer instructions, usually twenty to twenty-five minutes. Transfer to a freezer-safe container and freeze for at least four hours before serving.