Basque-Style Sweet Potato Cheesecake

2 lb. sweet potatoes (3–4 large), preferably garnet, scrubbed
Unsalted butter (for pan)
24 oz. cream cheese (not low-fat), room temperature
1 cup (200 g) granulated sugar
¼ cup (50 g) light brown sugar
3 large eggs
½ cup sour cream (not low-fat), room temperature
½ cup heavy cream, room temperature
1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt
1 vanilla bean, split lengthwise, or 2 tsp. vanilla extract
¼ cup (31 g) all-purpose flour
½ tsp. ground cinnamon
¼ tsp. ground ginger
¼ tsp. ground nutmeg

Place a rack in middle of oven and preheat to 450°F. Place sweet potatoes on a foil or parchment-lined rimmed baking sheet and roast, turning once, until skins are puffed and scorched in spots where the juices have bubbled out and caramelized and a skewer easily slides into flesh, 55–65 minutes. Let sweet potatoes cool slightly. Reduce oven temperature to 425°F.
Peel sweet potatoes; discard skins. Transfer flesh to a food processor and process until smooth (or, pass through a food mill into a large bowl). Let cool at least 1 hour.
Lightly butter pan. Cut 2 long lengths of parchment paper and crumple to soften (this will help it lay flatter in the round pan). Line pan with both sheets of parchment so they overlap in a crisscross manner; overhang should extend at least 2" above the rim. Beat cream cheese, granulated sugar, and brown sugar in a stand mixer fitted with the paddle attachment on medium speed, scraping down sides of bowl as needed, until very smooth, about 3 minutes. With motor running, add 2 cups sweet potato purée by spoonfuls (reserve any remaining purée for another use); beat until fully incorporated. Add eggs one at a time, beating well after each addition and scraping down bowl and paddle as needed. Reduce speed to medium-low and mix in sour cream, cream, and salt. Scrape in vanilla seeds or add vanilla extract. Turn off mixer and sift in flour, cinnamon, ginger, and nutmeg. Beat on low speed just to incorporate, about 30 seconds. Fold batter a few times with a rubber spatula, making sure to scrape bottom of bowl. Scrape batter into prepared pan; smooth surface.
Bake cheesecake until deeply bronzed and quite puffed on top but still with a pronounced wiggle in the center when gently shaken, 55–65 minutes. Transfer pan to a wire rack and let cheesecake cool, about 1½ hours.
To serve, carefully unmold cheesecake and peel away parchment before slicing.