Make the pastry crust

1. Place one oven rack in the lowest position and a second rack 5 to 6 inches from the broiler element. Pre-heat the oven to 350ºF or 325ºF Convection.
2. Whisk the flour, sugar, and salt together in a medium-sized bowl. Add the melted butter and stir with a wooden spoon until dough forms (about 15 seconds). Using your hands, press two-thirds of the dough into the bottom of a 10-inch tart pan with a removable bottom. Press the remaining dough into the fluted sides of the pan. Press and smooth the dough with your hands to an even thickness. (This part is fun and very much enjoyed by small helping hands).
3. Place the pan on a wire rack set in a rimmed baking sheet and bake on the lowest oven rack, until the crust is deep golden brown and firm to the touch (30 to 35 minutes), rotating the pan halfway through baking. Set aside until ready to fill.

Make the filling

1. Cut 6 apples lengthwise into quarters and cut each quarter lengthwise into 4 slices. Melt 1 1/2 tbsp butter in a 12-inch skillet over medium heat. Add the apple slices and water and toss to combine. You may need to work in batches. Cover and cook, stirring occasionally, until the apples begin to turn translucent and are slightly pliable (3 to 5 minutes). Transfer the apples to a large plate(s), spread into a single layer, and set aside to cool. Do not clean the skillet as you’ll be using it again in a few minutes to cook the filling.
2. While the apples cook, microwave the apricot preserves until fluid (about 30 seconds). Strain the preserves through a fine-mesh strainer into a small bowl, reserving solids. Set aside 3 tbsp of strained preserves for brushing the tart.
3. Cut the remaining 6 apples into 1/2 inch thick wedges. Melt the remaining 2 tbsp butter in the now-empty skillet over medium heat. Add the remaining apricot preserves, reserved apricot solids, apple wedges, and salt. Cover and cook, stirring occasionally, until the apples are very soft (about 10 minutes).
4. Mash the cooked apple mixture in the skillet to a puree with a potato masher (or a fork if you don’t have a potato masher). Continue to cook, stirring occasionally, until the puree is reduced to 2 cups (about 5 minutes).
5. Transfer the apple puree to the baked tart shell and smooth the surface with the back of a spoon or small spatula. Select the 5 thinnest slices of sautéed apple and set aside (they’ll form the centre of the flower, so they need to be particularly flexible). Starting at the outer edge of the tart, arrange the remaining slices, tightly overlapping, in concentric circles. Bend the reserved slices to fit in the centre. You may have some slices left over which you can snack on while you’re waiting for the tart to bake (they’re delicious).
6. Bake the tart, still on the wire rack in the baking sheet, on the lowest rack in the oven for 30 minutes. Remove the tart from the oven and heat the broiler.
7. While the broiler heats, warm the reserved apricot preserves in the microwave until fluid (about 20 seconds). Brush the preserves evenly over the surface of the apples, avoiding the tart crust. (If you get it on the edge of the tart crust it’ll be difficult to remove from the pan and wreck the pretty presentation).
8. Broil the tart, but watch it VERY carefully, turning as necessary until the apples are attractively caramelized (1 to 3 minutes).
9. Let the tart cool for at least 1 1/2 hours. Remove the outer metal ring of the tart pan, slide a thin metal spatula between the tart and pan bottom, and carefully slide the tart onto a serving platter. Or leave it on the tart bottom if it proves recalcitrant. Cut into wedges and serve.
10. Accept applause graciously.