Preheat your oven to 350°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 overmix.
Pour the mixture into the prepared pie plate.
Bake until the cake isn't liquid anymore but still a bit jiggly, for 30-35 minutes.
Transfer the cake to a cooling rack and cool to room temperature for about 2 hours. Refrigerate it for at least 4 hours, 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. Alternatively, cube the cream cheese and microwave it for 20 seconds, and submerge the eggs in a bowl of warm (not hot) water.
How long you bake the cake will depend on the pan you use and your oven. In my old oven, using an 8-inch pan, it needed 40 minutes. In the new one, which is more accurate, and when using a 9-inch pan, it needs just 30 minutes. Both are excellent, so it's up to you which pan you use. Just remember to start checking after 30 minutes and try not to over-bake.
You can keep the leftovers in the fridge, in an airtight container, for up to five days. Remove them from the fridge an hour before serving.