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In a medium bowl, beat heavy cream until it begins to thicken. Add powdered sugar, and beat heavy cream until stiff peaks form. Set aside.
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In a large bowl, beat together cream cheese, 1/4 cup sugar, and vanilla until smooth. Add pumpkin puree, cinnamon, nutmeg, ginger, and all spice; beat until smooth. Fold whipped cream into pumpkin mixture until well combined.
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Refrigerate about 4 hours, or until cheesecake is firm.
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When cheesecake is set, heat 1/2" oil in a large skillet over medium-high heat.
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Mix 1/2 cup sugar and 1 tablespoon cinnamon in a bowl, and pour evenly onto a plate. Set aside.
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Place about 1/4 cup cheesecake on the lower 1/3 of a tortilla. Fold the bottom edge up away from you and over the filling, then fold in both side edges, and finally roll the burrito away from you until closed.
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Fry the burritos in hot oil for 30 to 45 seconds per side, until the tortilla is crispy and golden.
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Immediately transfer to a paper towel lined plate, and drain briefly. Roll each chimichanga in the cinnamon-sugar mixture. Place chimichangas on a plate to rest.
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Refrigerate chimichangas at least 2 hours (to overnight) to let the filling set up again.
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To serve, cut chimichangas in half at an angle with a serrated knife and drizzle with caramel sauce, if desired.