Karamelläpple Monkey Bread

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1. 1
   Mix 4 large eggs, one ¼-oz. envelope instant yeast (about 2¼ tsp.), 4 cups plus 2 Tbsp. (516 g) all-purpose flour, ⅓ cup apple cider, 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt, 1 Tbsp. light brown sugar, and 1 Tbsp. vanilla extract in the bowl of a stand mixer fitted with a dough hook on low speed until a shaggy, stiff dough forms around hook, about 4 minutes. With motor running, add 1 cup (2 sticks) unsalted butter, cut into pieces, room temperature, 1 piece at a time, mixing until almost completely incorporated after each addition before adding more, until all of the butter has been added, about 5 minutes total. Increase speed to medium and mix until dough is soft, smooth, and elastic, about 5 minutes. (Dough should not be sticking to the sides of the bowl but might still stick to the bottom.) Tightly cover bowl with plastic wrap and let dough sit at room temperature until puffy and almost doubled in size, about 1½ hours.
2. 2
   Meanwhile, coat pan with nonstick vegetable oil spray. Bring 3 cups apple cider to a boil in a large Dutch oven or other heavy pot and cook until reduced to a syrup-like consistency (similar to honey), 18–22 minutes. (There should be just a thin layer left in the pot.)
3. 3
   Add ½ cup plus 2 Tbsp. (packed; 125 g) light brown sugar, ¼ cup heavy cream, 2 Tbsp. unsalted butter, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, ½ tsp. vanilla extract, and ¼ tsp. ground cinnamon to cider in pot and bring to a boil, stirring until butter and sugar are melted. Continue to cook until mixture has thickened slightly and bubbles are large, 2–3 minutes. Immediately pour caramel into prepared pan; set aside. Reserve pot (no need to wash it out).
4. 4
   Toss 1½ lb. Honeycrisp apples (about 4 large), peeled, cut into 2" pieces, ⅓ cup apple cider, ¼ cup (packed; 50 g) light brown sugar, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 1 tsp. ground cinnamon in reserved pot to combine (it’s okay if there is a decent amount of caramel stuck to pot). Place over medium-high heat and cook, stirring often, until apples are fork-tender and liquid is mostly evaporated, 7–10 minutes. Remove from heat and set aside.
5. 5
   Toss together remaining 1 cup (packed; 200 g) light brown sugar, 1 Tbsp. ground cinnamon, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a medium bowl. Place ½ cup (1 stick) unsalted butter, melted, in another medium bowl.
6. 6
   Punch down dough and transfer to a surface lightly dusted with all-purpose flour. Press dough into about a 1"-thick slab and cut into 1½" pieces. Working with 1 piece of dough at a time, toss in melted butter to coat, then in cinnamon sugar and stack on top of caramel in reserved pan, intermittently adding pieces of cooked apples throughout. (If there is any liquid left in pot, discard.) Cover pan with plastic wrap and let sit at room temperature until dough balls are puffy and spring back when gently pressed, about 45 minutes.
7. 7
   Just before dough is ready, place a rack in middle of oven; preheat to 350°.
8. 8
   Place pan on a rimmed baking sheet, remove plastic, and bake monkey bread until top is golden brown and an instant-read thermometer inserted into the center registers 190°, 40–45 minutes. Let cool 20 minutes (set a timer), then run an offset spatula around sides of pan to loosen and invert monkey bread out onto a platter.