Peel and core all of the apples. Place them in cold water with the juice of a lemon to prevent them from browning while you slice them.
1/2 of the apples will be cut into thin slices for the top of the filling. Cut 1/2 of the apples into 16 slices. Keep the remaining 1/2 of the apples in the lemon water while you cook the decorative slices.
Melt 1 Tablespoon butter in a large skillet over medium heat. Add apple slices and 1 Tablespoons water to the skillet and toss. Cover and cook, stirring occasionally, until apples begin to turn translucent and are slightly pliable. About 5 minutes. Spread apples in a single layer on a tray or large plate. (This prevents them from browning) While the apples are cooking make the apricot glaze. (Don't bother to clean the skillet, you'll use it again to cook the remaining apples)
The other 2 1/2 pounds of the apples will be cooked and mashed to make the base of the filling. Cut the remaining apples into 1/2" wedges.
Melt remaining 2 Tablespoons butter in the skillet over medium heat. Add apples, any remaining apricot preserves and solids to the sauce pan and cover. Cook, stirring occasionally until apples are very soft, about 10 minutes.
Mash the apples with a food processor or immersion blender until they are pureed. Continue to cook the puree until it's reduced to about 2 cups, about 5-7 minutes.
Spread puree on the cooked tart shell. Reserve the most pliable apple slices for the center of the pie.
Place the apple slices around the edge of the tart, working towards the center, using the thinnest for the very center of the tart.
Bake tart, still on wire rack and baking sheet, on the lowest rack of the oven for 30 minutes. Remove tart from oven and heat broiler.
Heat up the remaining 3 Tablespoons of the apricot glaze in the microwave, until liquid, about 20 seconds. Brush the thinned glaze on the apples, avoiding the crust.
Place tart on the upper rack and broil for 30 seconds at a time, watching carefully, turning each time, until the tart caramelizes on the edges, about 1-3 minutes total.
Allow the tart to cool for 1 1/2 hours before transferring tart to serving plate or cake stand.