- In a small bowl, whisk together ½ cup milk and cornstarch until smooth. Set aside.
- In a small saucepan set over medium heat, heat remaining milk just until simmering. Set aside.
- Make the caramel: In a heavy saucepan over medium heat, stir brown sugar and water together until all sugar dissolves. Increase heat to high and cook without stirring until an instant-read thermometer reads between 210 and 215 degrees.
- In a large, heatproof bowl, combine egg yolks and pumpkin purée and whisk. Gradually whisk in hot milk—slowly at first, to temper yolks—then add cornstarch mixture. Slowly pour caramel into bowl while whisking to combine.
- Have large, heatproof pitcher ready. Return custard to saucepan. Cook over medium heat, whisking constantly, until custard thickens and an instant-read thermometer registers 175 degrees, about 3 to 5 minutes. The consistency should be similar to thick pudding. Remove from heat. Whisk in butter, vanilla, rum, and salt. Pour into the heatproof pitcher.
- Pour ½ cup custard into four prepared jars. Cover with plastic wrap and chill until set, approximately 3 to 5 hours. Before serving, top each with salted caramel sauce cinnamon cream.
Salted Caramel Sauce
- Pour cream into a small pitcher. Scrape vanilla seeds from pod and add both pod and seeds to pitcher. Set aside.
- Place sugar in a medium, heavy-bottomed saucepan. Over medium heat, stir constantly and vigorously with wooden spoon. Once sugar has completely melted and turned amber in color, add butter pieces one at a time. Whisk until butter has completely melted before adding another piece. Whisk for approximately 3 seconds, then slowly pour vanilla cream into pot. Whisk until smooth. Add salt and whisk to combine. Strain into a heatproof bowl and let cool slightly. Reserve.
In the bowl of a stand mixer fitted with whisk attachment, combine all ingredients and whip until stiff peaks emerge. Reserve.