For The Tart Shell:

Preheat the oven to 350 degrees.

In the bowl of an electric mixer fitted with a paddle attachment, mix the butter and sugar together until they are just combined.

Add the vanilla. In a medium bowl, sift together the flour and salt, then add them to the butter-and-sugar mixture.

Mix on low speed until the dough starts to come together. Dump onto a surface dusted with flour and shape into a flat disk

Press the dough into a 13 3/4″ x 4 1/2″ x 1″ high rectangle false-bottom tart pan, making sure that the finished edge is flat.

Chill until firm.

Line the tart pan with parchment paper. Fill with beans or rice. Bake for 20 minutes.

Remove the foil and beans, prick the tart all over with the tines of a fork, and bake again for 20 to 25 minutes more, or until lightly browned.

Cool to room temperature.

Make the filling:

In a small bowl combine lime juice and mint. Using the end of a wooden spoon or the end of a lemon reamer, muddle the mint until broken down by pressing down and twisting. 

Use a fine-mesh strainer to strain the mint particles from the lime juice. Discard mint. 

In a medium bowl, whisk together sweetened condensed milk, egg yolks, and cream cheese until smooth. Add lime juice, zest, and rum. Mix until well incorporated. 

Pour into the baked crust and bake in a preheated 350-degree oven until just set in the middle, 15 minutes. 

Let cool at room temperature, then refrigerate until firm, at least 2 hours.

Serve with whipped cream and garnish with mint leaves and slices of fresh lemon.