Place the cream cheese in a medium heatproof bowl; set aside.

In another medium heatproof bowl, whisk together egg yolks and 6 tablespoons sugar; set aside.

In a medium saucepan over medium-high heat, combine the cream, milk, and 6 tablespoons sugar.

Stir until the mixture approaches a bare simmer, and reduce heat to medium.

Scoop 1/2 cup of the hot cream mixture and slowly pour the hot mixture into the egg yolks, whisking the eggs constantly.

Repeat, adding another 1/2 cup of hot cream to the bowl with the egg yolks.

Using a heatproof spatula, stir the cream in the saucepan as you slowly pour the egg-and-cream mixture from the bowl into the pan.

Cook the mixture over medium heat, stirring constantly and scraping the bottom as you stir, until the mixture thickens, coats the back of the spatula and reaches a temperature of 170 to 175 degrees F.

Pour the custard through a fine-mesh strainer into the bowl with the cream cheese.

Whisk until smooth, then set the bowl into an ice water bath, stirring the base occasionally until it is cool.

Remove from the ice water bath, cover with plastic wrap and refrigerate mixture overnight.

After the mixture has chilled, stir together strawberries and remaining tablespoon of sugar in a medium bowl.

Let the berries stand at room temperature for 30 minutes.

Add vanilla to ice cream mixture; stir to combine.

Freeze ice cream mixture in your ice cream machine according to the manufacturers instructions.

Fold strawberries into ice cream and freeze for at least 4 hours.

Top with graham cracker crumbs before serving, as desired.