Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch pie pan.
Heat apricot jam, brown sugar, and heavy cream in a small saucepan until mixture is well combined and simmering, about 6 minutes. Let jam mixture cool, 20 to 25 minutes.
Roll out puff pastry onto a lightly floured surface; press into an even layer in the pie pan to form the base of the tart. Cover the tart with apple slices by overlapping them across the tart. Scatter cubed butter evenly over the apples; pour the jam mixture over the tart.
Bake in the preheated oven for 30 minutes. Turn the pan and sprinkle sliced almonds over the tart. Continue to bake until the the top starts to bubble, about 30 minutes more.