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1
Spread the pumpkin puree on a couple of layers of paper towels to dry out a bit. It's suggested about 2 hours...I've left it up to 15 hours and it was fine.
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2
Preheat your oven to 350 degrees F. Butter a 9-inch nonstick springform pan. I like to butter even though it's nonstick...I hate sticking. If you don't have a springform pan, don't fret. This will still work in a similar-sized dish. I used a pie dish until I got a springform pan, because I typically don't make cheesecake, and it worked fine. You just don't see that pretty side view of the crust. It's a little easier to cut the springform cheesecake as well (if you're looking for a reason to invest in one).
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3
Put the graham crackers, pecans (you can omit, just add 2 more graham crackers to the mix) and brown sugar in a food processor and pulse until the mixture becomes a fine crumb. Drizzle the butter on top and pulse until just mixed. Press the mixture into the bottom of either the springform or the pie pan. Place the crust in the oven for 10 minutes or until it starts to turn a little golden. Don't walk away and do something else here. It can happen fast and you don't want it to burn. When done, set the crust aside for a bit to cool.
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4
Put the cream cheese and sugar in an electric-stand mixer fitted with the paddle attachment and beat the cream cheese on low-medium until smooth. A couple of notes here... First, if you don't have an electric-stand mixer you can use your beautiful arms and a spatula to beat it into submission. That's how I did it when I was hanging in the PRC. Second, you don't want to add too much air, at any point, into this creamy mixture we're creating right now. Too much air can make unsightly cracks on your cheesecake. Thus keep it to a low-speed beating as much as possible. I don't want you to panic about this now, because we have the awesome salted caramel to mask any of the above-mentioned fissures. But still, the goal is no cracks.
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5
Once the cream cheese is smooth, add the salt and the five-spice powder while the machine is on low.
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6
Scrape the pumpkin off of the paper towels and in with the cream cheese. Mix until completely combined. Add the eggs, one at a time, making sure they are completely incorporated before you add the next. Keep your machine on low here and continue to scrape down the sides of the bowl so that everything becomes a part of the mix.
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7
Lastly, throw in the cream, Satsuma juice and the vanilla. Mix until everything is co-mingled and smooth.
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8
Pour the mixture on to the cooled crust. Place in the oven. Check after 50 minutes. The center will wiggle, but should not be liquid. Cook a little longer if it looks too jiggly. It shouldn't take more than 60 minutes. Cool for a couple of hours at room temperature. When cool to the touch, cover with plastic wrap and place in the fridge.
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9
When ready to make the salted caramel, place the butter and brown sugar in a sauce pan on medium-heat and whisk away until the sugar has melted. Pour in the heavy cream, 1/2 teaspoon of salt and vanilla (save the coarse salt for serving time). Bring to a boil and then reduce to a simmer for 5-ish minutes. Continue to whisk and stir as it cooks. You want the caramel to thicken. Set aside to cool or refrigerate until ready to use.
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10
At dessert time, take the side of the springform pan off...you may need a knife to gently run along the side. If so, do this near the sink so that you can run the knife under hot water periodically so that the cheesecake doesn't stick.
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11
If the caramel was refrigerated, place it in a microwave-safe bowl and microwave until just warmed a bit through. You don't want it too hot and runny. I did it for about 15 seconds in my microwave. Let it cool just a hair (5 minutes). Pour the caramel on top of the cheesecake. It should form a pond in the center, leaving about 2 centimeters around the edges. Voile. If you had any cracks, they are now mysteriously gone. No one will ever know. Sprinkle the 1/2 tablespoon of coarse salt over the top. Done. Pour yourself a mason jar of cognac to go with your slice. You done good.
