Special equipment: a 10-inch tart pan with a removable bottom; pie weights
For the crust: In a large bowl, beat together the butter and sugar with an electric mixer on medium-high speed until light and fluffy, about 3 minutes. Add the salt, egg and cream; beat until incorporated. Add the flour and beat until a dough comes together. Form the dough into a disc and then press it evenly into the bottom and up the sides of a 10-inch tart pan with a removable bottom; if necessary, use a piece of plastic wrap to help keep the dough from sticking. Refrigerate until firm, about 1 hour, or freeze for 30 minutes.
Preheat the oven to 350 degrees F. Line the tart crust with foil and fill with pie weights. Bake until the edges of the crust look set and just barely golden, about 15 minutes. Carefully remove the foil and pie weights, and continue to bake until the crust is golden brown all over, about 20 minutes more. Cool completely.
For the filling: In a large bowl, combine the cream cheese, sugar and vanilla, and beat with an electric mixer until soft and very creamy, 1 to 2 minutes. Add the cream and continue beating until the mixture holds stiff peaks, stopping occasionally to scrape the bowl with a rubber spatula, 2 to 3 minutes more.
Spoon the cream cheese mixture into the cooled tart shell and smooth with an offset spatula. Top with the berries.
Combine the apricot preserves and a splash of water in a small bowl and microwave until warm, about 45 seconds. Strain through a sieve into another bowl. Gently brush or spoon the apricot glaze over the berries.
Serve the tart immediately, or refrigerate for up to 3 hours.