Mexican Chocolate Ice Cream

This is straight from the Ben & Jerry's cookbook, except I cook the mixture because I worry about raw eggs. It makes one quart this way, but I doubled it for more people and because more mixture works better in a larger ice cream maker.

1/4 C unsweetened cocoa
3/4 C sugar
1 and 1/2 C milk
2 eggs
1 oz dark or unsweetened chocolate, chopped
1 C heavy or whipping cream
1 tsp vanilla extract (Mexican?)
1/2 Tbsp cinnamon
1 and 1/2 C crumbled gingersnap pieces

Mix cocoa, sugar, milk, and eggs in saucepan. Bring to a boil. Remove from heat and stir in chocolate. Stir in cinnamon, vanilla, and cream. Cool for a few hours in fridge (with plastic wrap pressed on the surface of the custard). Mix in ice cream maker according to directions. Add cookie pieces during last two minutes of mixing time.