Add the egg yolks and granulated sugar to a bowl and vigorously whisk or beat with an electric mixer until fluffy and pale yellow.
Add the whole milk, vanilla extract, and salt to a saucepan and heat to a gentle simmer. Do not boil.
Pour the warm milk into the egg yolk mixture while whisking or mixing with an electric mixer so the yolks don't curdle.
Pour everything back into the saucepan and cook, stirring frequently, until starting to bubble and thicken slightly. It should be 170°F on a digital instant read thermometer and thick enough to coat the back of a spoon.
Remove from heat and strain the custard through a sieve and into a bowl. Allow to cool completely. You can place the bowl over an ice bath to speed up the cooling.
In a large bowl, use an electric mixer to beat the heavy whipping cream until thick and fluffy. Fold the whipped cream into the cooled custard.
If making with an ice cream maker: Churn the ice cream as instructed by your ice cream maker until thick with a consistency of soft serve. Add the crushed Oreo cookies and churn until evenly distributed. Transfer the ice cream to a bowl or a 9 x 5" loaf pan and cover the top with plastic wrap. Freeze for 1-3 hours or until frozen to your desired consistency.
If making without an ice cream maker: Fold the crushed Oreo cookies into the ice cream and transfer to a bowl or a 9 x5" loaf pan. Cover the ice cream with plastic wrap. Touch the plastic wrap to the surface of the ice cream to prevent ice crystals from forming. Freeze for 6 hours or overnight.