Pour the half-and-half into a heavy saucepan. Add the sugar and stir to combine. Bring the mixture to a simmer over low heat, stirring occasionally.
In a separate bowl, beat the egg yolks until they're light yellow in color. Temper the egg yolks by slowly drizzling in about 2 cups of the hot half-and-half mixture while whisking quickly. Pour the tempered egg yolk mixture into the saucepan, whisking gently as you add it. Simmer over low heat until it gets very thick, 5 to 7 more minutes.
Pour the mixture through a fine mesh strainer into a medium bowl, pressing with a spoon or spatula to gently force it through. Pour in the heavy cream, then stir to combine. Stir in vanilla. Cover and refrigerate this mixture until it's totally cool.
Freeze the mixture in an ice cream maker according to its directions. After the cycle is completed, stir in the crushed oreos and immediately transfer to a freezer container and place in the freezer. A couple of hours later, open the container and stir again to make sure the candies are distributed.
Freeze for another 24 hours or until frozen hard and solid.