In a large mixing bowl, whisk together the 1 ¼ cups all-purpose flour, ¾ cup granulated sugar, and 1 pinch fine sea salt. Add the cold 4 tbsp unsalted butter cut into small pieces cubes and use your fingertips (or a pastry cutter) to rub the 4 tbsp unsalted butter cut into small pieces into the 1 ¼ cups all-purpose flour until the mixture resembles coarse, pea-sized crumbs — some larger bits of unsalted butter cut into small pieces are fine and desirable.

Drizzle in the 3 tbsp ice water plus more if needed one tablespoon at a time, stirring with a fork after each addition, just until the dough begins to clump together. It should hold when pressed but not feel wet or sticky. Tip it onto a lightly floured surface and bring it together into a flat disk. Wrap in plastic wrap and refrigerate for at least 20 minutes (or up to 2 days).

Peel, core, and quarter the 2 ½ lb firm apples such as Granny Smith. If using large firm apples such as Granny Smith, cut each quarter in half lengthwise (into eighths). Pat them dry with paper towels — removing excess moisture helps the caramel concentrate properly.

Place a 10-inch oven-safe skillet (cast iron or stainless steel) over medium heat. Spread the ¾ cup granulated sugar in an even layer across the bottom. Cook without stirring, swirling the pan gently once or twice, until the ¾ cup granulated sugar melts and turns a deep amber color, about 8–10 minutes. Watch carefully — it can go from perfect to burnt quickly.

Remove the pan from heat and immediately add the 4 tbsp unsalted butter cut into small pieces pieces and 1 pinch fine sea salt. Stir carefully — the mixture will bubble vigorously. Return to low heat and stir until the 4 tbsp unsalted butter cut into small pieces is fully melted and the caramel is smooth. Stir in the 1 tsp pure vanilla extract if using.

Arrange the 2 ½ lb firm apples such as Granny Smith pieces tightly in the caramel, standing them on their edges in concentric circles, packing them in snugly — they will shrink as they cook. Start from the outside edge and work inward. It will look like too many 2 ½ lb firm apples such as Granny Smith at first; that's exactly right.

Cook the 2 ½ lb firm apples such as Granny Smith over medium heat for 20–25 minutes, occasionally pressing them down gently with a spatula, until the caramel is thick and bubbling around the edges and the 2 ½ lb firm apples such as Granny Smith are just tender when pierced with a knife. Remove from heat and let cool for 10 minutes.

While the 2 ½ lb firm apples such as Granny Smith cook, preheat your oven to 400°F. On a lightly floured surface, roll the chilled dough into a circle roughly 11–12 inches in diameter (about 1/8 inch thick) — just slightly larger than your skillet.

Drape the pastry circle over the rolling pin and carefully lay it over the 2 ½ lb firm apples such as Granny Smith in the skillet. Tuck the edges of the dough down around the inside of the pan, like tucking in a blanket. Use a fork or knife to poke 4–5 small steam vents in the top.

Transfer the skillet to the oven and bake for 25–30 minutes, until the pastry is deep golden brown and the caramel is visibly bubbling at the edges.

Remove from the oven and let the tart rest in the pan for exactly 5–10 minutes — no longer, or the caramel will set and the tart will stick. Place a large, flat serving plate (with a rim to catch any caramel drips) upside-down over the skillet. In one confident motion, flip the skillet and plate together. Lift the skillet off slowly. If any 2 ½ lb firm apples such as Granny Smith pieces have shifted, use a spoon to nudge them back into place.

Serve warm, cut into wedges, with a scoop of vanilla ice cream or crème fraîche or a generous spoonful of crème fraîche. The tart is best enjoyed within a few hours of baking.