Warm the condensed milk, 1 cup milk and sugar in a sauce pan over medium heat. Stir in the vanilla extract and set aside to cool slightly.

Pour the remaining 1 cup milk in a large bowl. In a separate bowl, whisk together the egg yolks. Temper the egg yolks by adding 1/2 cup of the warm mixture, whisking constantly. Add another 1/2 cup and whisk. Then add back the egg yolk mixture into the sauce pan with the remainder of the warm mixture.

Stir the mixture over medium heat with a heatproof spatula. My mixture didn't thicken so after a few minutes I whisked 2 teaspoons of corn starch. It still didn't thicken but I had to continue cooking for another couple of minutes to make sure the corn starch would cook through.

Place a strainer over the bowl of remaining milk and pour the warm mixture over it. Chill the mixture for several hours or overnight.

Process the mixture in your ice cream maker according to manufacturer's instructions. About 20 minutes in, I added the brownie chunks into the churning mixture and continued to let it churn for another 10 minutes. Chill for a few hours before serving.