For the “Burnt” Sugar Caramel: Weigh out the sugar for the caramel along with the water and lemon juice.
Combine the milk and cream from the ice cream base in a pot that can fit the ingredients comfortably and that has enough room to expand when the hot sugar is added (typically about twice the volume of the liquid); place over medium-high heat.
In a separate pot, combine the sugar with the water and lemon juice (to prevent crystallization) and cook over high heat until the sugar begins to smoke but does not literally burn (170°C / 338°F; do not confuse steam with smoke!).
Slowly pour the hot milk-cream mixture into the sugar while whisking constantly. This will result in the “burnt” caramel component. The liquid does not need to cool down; in fact, it will make the process a lot faster if it is used as soon as the caramel is made.
For the Ice Cream Base: Make the ice cream base according to the Classic Ice Cream Method.
Strain the base through a fine-mesh strainer and cool over an ice bath. Age the base under refrigeration overnight.
Once the base has aged, churn to the desired consistency.
Harden for at least 2 hours and up to 4 hours. Reserve until needed.