Prepare custard base: Pour milk and cream into a pan, add small amount of sugar, and gently warm on medium-low heat until simmering.
Temper egg yolks: Whisk egg yolks in a bowl. Gradually add a small amount of warm milk mixture to yolks while whisking to temper, then pour yolk mixture back into the pan.
Cook custard: Cook the mixture over medium-low heat, stirring constantly, until the temperature reaches 82°C (180°F). Do not exceed this temperature to avoid curdling.
Strain custard: Pour custard through a fine mesh sieve into a mixing bowl to remove any coagulated bits.
Make caramel: In a small pan, add the large amount of sugar and a little water. Heat on high until sugar caramelizes and starts to smoke lightly or reaches 180°C (356°F). Remove from heat immediately.
Add butter and salt to caramel: Quickly stir in cubed butter and sea salt into the hot caramel until fully combined.
Combine caramel with custard: Immediately whisk the warm custard into the caramel mixture until smooth and fully incorporated.
Cool and age custard: Cover the custard with plastic wrap directly on the surface to prevent crust formation. Cool to room temperature, then refrigerate overnight to allow flavors to develop.
Strain before churning: Before churning, strain the custard again through a fine sieve to ensure smoothness.
Churn ice cream: Pour the custard into a pre-cooled ice cream machine and churn according to the manufacturer's instructions, typically 15-20 minutes, until it reaches a soft serve consistency.
Freeze to firm up: Transfer the churned ice cream to a freezer-safe container and freeze for at least 2 hours to achieve scoopable firmness.