In a medium bowl, stir in crushed graham cracker, granulated sugar, and melted butter with spatula until incorporated.

Press the crumb mixture into the pan, spreading it about 2 inches up the side. Press flat. Cover with plastic wrap and chill in the refrigerator for at least 30 minutes. (The crust can be made ahead) 

In a large saucepan, heat heavy cream, milk, and salt over medium-low heat until it begins to simmer. Turn off the heat.

In a medium bowl, whisk egg yolks with granulated sugar until well combined and light in color. Add one or two ladles of cream mixture into the egg yolks while whisking constantly.

Pour the egg yolks mixture back into the saucepan, and cook until it thickens up with low heat. Stir constantly and scrape the bottom and sides of the pot with a wooden spoon until it is thickened enough to coat the back of the spoon. (Do not boil or the egg yolks will curdle)

Let the mixture cool slightly. Stir in cream cheese over a strainer into the cream mixture until it dissolves. Let it cool completely.

Stir in lemon juice, lemon zest, vodka, and vanilla extract until incorporated.

Cover the mixture and chill for 6 hours or overnight.

Pour the freshly-churn ice cream over the crust. Tap the pan on the counter to get air bubbles out. Cover and freeze for at least 4 hours to firm it up.

Wash strawberries, remove the stems, and chop strawberries into smaller chunks. Put it into a medium saucepan.

Stir in lemon juice and sugar. Let it sit for at least 20 minutes until the water comes out from the strawberries.

Cook strawberry mixture over medium heat until it boils and the strawberry chunks get soft, stirring often.

Let the mixture cool down in the saucepan for 15-20 minutes.

Loosen and remove sides of springform pan. Pour strawberry jam over the ice cream cake. Arrange strawberries on top with pointed ends up.