Add the pineapple, jalapeno, lemon juice, and beer to a blender. Blend on high until well pulverized. Pass through a strainer to remove all the fibers, return to the blender (without straining the fibers, the ice cream can taste a little vegetal).
Add the eggs, yolks, salt and both kinds of sugar to the blender, blend on high until well combined.
Add the cream and milk to a saucepan over medium heat. Heat until it starts to bubble around the edges. While the mixer is running, add the hot cream to the mixer.
Return the mixture to the pot. Simmer until slightly thickened, about 5 minutes.
Add to an airtight container. Refrigerate until chilled, about 3 hours.
Churn in an ice cream maker according to manufactures specifications.