Preheat your oven to 350 degrees F. Generously grease a 9-inch pie plate with butter.
In a food processor, add the cream cheese, pumpkin, sweetener, vanilla, cinnamon, and coconut flour. Process until blended, stopping to scrape the sides of the bowl as needed.
Add the eggs and process just until blended. Don't over mix.
Pour the mixture into the prepared pie plate.
Bake until the cake isn't liquid anymore but is still a bit jiggly, 30-35 minutes.
Transfer the cake to a cooling rack and cool to room temperature, about 2 hours. Then cover and refrigerate for at least 4 hours, and preferably overnight, before slicing.
To slice the cake, use a sharp knife dipped in hot water and wiped clean. Dip it again after each slice. This will help you cut the cake into neat slices.
The cream cheese and the eggs should be at room temperature. You can take them out of the fridge a couple of hours ahead of time. Or cube the cream cheese and microwave it for 20 minutes, and submerge the eggs in a bowl of warm (not hot) water. How long you bake the cake will largely depend on the pan you use and on your oven. In my old oven, using an 8-inch pan, it needed 40 minutes (you can see how tall the cake was in the photos). In the new one, which I believe is more accurate, and using a 9-inch pan, it needs just 30 minutes - you can see it's flatter in the video. Both are excellent, so it's really up to you which pan you use. Just remember to start checking after 30 minutes and try not to over-bake.