Add the heavy cream, milk, and jalapeños in a heavy-bottomed pot and bring to a simmer over medium-high heat. Then remove from the heat to let the jalapeños steep in the milk mixture, about 15 minutes.

Strain the mixture through a sieve to remove the jalapeños and the film which may form on top.

Clean the pot and put the milk mixture back into it.

Add the sugar and egg yolks to a mixing bowl and whisk until pale yellow.

Slowly add a ladle of the milk mixture into the egg mixture while whisking to keep it from curdling. I like to add a wet towel or rag underneath the bowl with the egg mixture to keep it from moving around.

Add enough of the milk mixture that the egg mixture is thinner. Add it back into the pot with the remaining milk mixture.

Prepare an ice bath. I like to take a wide and shallow mixing bowl, fill it with ice and some water, and place another bowl (taller and less wide) in it.

Put the pot with the egg/milk mixture on medium heat and whisk continuously to keep from burning and until slightly thickened (the mixture will start to simmer and bubble).

Immediately pour into the bowl in the ice bath. Let cool and add the tequila and vanilla. Put the mixture in the fridge overnight to make it cold.

Add the batter, lime zest, and lime juice into the ice cream maker. Churn the batter according to the instructions of your ice cream maker.