BUTTERNUT SQUASH TARTE TATIN

Steps:

• Do ahead:
• Place a rack in upper third of oven; preheat to 350°F. Butter a 10" springform pan or cake pan and line bottom with a parchment paper round. Cut off neck from squash. Peel neck and bulb until you reveal the orange flesh underneath (you might need to take off a few layers). Slice both pieces in half lengthwise; scoop out seeds. Slice all squash pieces crosswise 1/4" thick. Arrange on a rimmed baking sheet. Melt 3 Tbsp. butter in a small saucepan and drizzle over squash. Sprinkle with ¼ cup granulated sugar and a pinch of salt and toss to coat. Arrange squash in a single layer (use a second rimmed baking sheet if needed) and roast until tender and just starting to curl around the edges but not yet browned, 30-35 minutes. Let cool. Carefully move oven rack to highest position and increase oven temperature to 400°.
• Meanwhile, cut remaining 3 Tbsp. butter into pieces and set aside. Bring lemon juice, 3/4 cup granulated sugar, and 3 Tbsp. water to a boil in a large saucepan over medium-low heat, stirring with a heatproof rubber spatula until sugar is dissolved. Continue to cook, swirling pan often (do not stir), until caramel is light amber in color, 6-8 minutes. Remove from heat and add reserved butter a piece at a time, stirring after each addition until incorporated and smooth. Once all the butter has been added, stir in vanilla and remaining 1/4 tsp. salt. Pour caramel into prepared springform pan and tilt to coat bottom. Let cool.
• Starting with slices from the neck, layer squash in an overlapping rosette pattern over caramel. Sprinkle with 1 Tbsp. granulated sugar. Arrange remaining squash over first layer, placing pieces wherever needed to create an even thickness of squash across entire tart (this layer doesn't need to be pretty since it won't be visible). Sprinkle with remaining 1 Tbsp. granulated sugar and chill while you roll out the puff pastry.
• Let pastry sit at room temperature about 4 minutes to soften slightly. Roll out on a lightly floured surface, dusting with more flour as needed to prevent sticking and rotating a few times, to a round that's a little over 11". Using pan as a template, trim excess dough to make an 11" round. Using a fork, prick pastry in 12-15 places. Drape pastry over squash and use a spoon to tuck edges in slightly between squash and sides of pan.
• Bake tarte Tatin 20 minutes. Reduce oven temperature to 350°F and continue to bake until pastry is puffed and golden brown, 45-50 minutes. Transfer to a wire rack and let cool in pan 10 minutes.
• If using a springform pan, remove ring and carefully invert tarte Tatin onto rack (take care as some of the hot caramel could drip). If using a cake pan, set rack upside down over pan and invert tarte Tatin onto rack. Let cool 20 minutes.
• Meanwhile, whisk cream in a small bowl to soft peaks. Beat in powdered sugar and cinnamon.
• Serve tarte Tatin warm topped with dollops of cinnamon whipped cream.
• Do Ahead
• Tarte Tatin can be baked 10 hours ahead. Store loosely wrapped at room temperature. Reheat in a 250°F oven.