Prepare the pastry dough by combining flour, 3 tablespoons sugar, and salt in a large bowl. Cut in the cold butter using a pastry cutter or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces remaining.
Add ice water one tablespoon at a time, stirring gently with a fork until the dough just begins to come together. Be careful not to overwork the dough—this ensures your crust will be flaky.
Form the dough into a disk, wrap it in plastic, and refrigerate for at least 30 minutes or up to 2 days. This resting period allows the gluten to relax and the butter to chill properly.
Preheat your oven to 400°F (200°C) and position a rack in the center. If using a baking sheet, line it with parchment paper.
Core and slice the apples thinly (about ⅛ inch thick), keeping the skin on for color and texture. If using lemon juice, toss the slices with it to prevent browning.
Roll out the chilled dough on a lightly floured surface into a 12-inch circle about ⅛ inch thick. Transfer to your tart pan or baking sheet.
Arrange apple slices in an overlapping pattern, starting from the outside and working toward the center, leaving about a 1.5-inch border around the edge.
Fold the pastry border over the edge of the apples, pleating as necessary to create a rustic look. The center of the tart should remain open with the fruit visible.
Sprinkle the arranged apples with the remaining sugar and cinnamon (if using), then dot with the 2 tablespoons of butter pieces.
Bake for 45-50 minutes until the crust is golden brown and the apples are tender and caramelized at the edges. Rotate the pan halfway through for even browning.
Prepare the glaze by heating the apricot jam with 1 tablespoon of water in a small saucepan until it becomes liquid, then strain if chunky.
Brush the warm glaze over the apples immediately after removing the tart from the oven for a beautiful shine and added flavor.
Allow the tart to cool for at least 15 minutes before slicing to let the juices set slightly. Serve warm or at room temperature.