In a food processor, combine the flour, butter, sugar, cardamom, and salt. Pulse until the mixture resembles coarse crumbs.
Add 2-3 tablespoons of cold water and pulse until the dough comes together. If needed, add more water, 1 tablespoon at a time.
Transfer the dough to a lightly floured surface and shape it into a disk. Wrap in plastic wrap and refrigerate for at least 30 minutes.
Preheat the oven to 375°F (190°C).
On a lightly floured surface, roll out the dough into a circle that is about 12 inches (30 cm) in diameter.
Transfer the dough to a tart pan and press it evenly into the bottom and sides. Trim off any excess dough.
Arrange the mango slices in a circular pattern on top of the dough.
Brush the mango slices with lemon juice to prevent browning.
Bake the tart in the preheated oven for 25 minutes, or until the crust is golden brown.
Remove the tart from the oven and let it cool for a few minutes.
Brush the mango slices with the melted apricot jam to glaze.
Serve the tart warm or chilled.