Preheat the oven to 350 degrees F (177 degrees C). Line a 9x9 in (23x23 cm) baking pan with parchment paper.
Using a bowl in the microwave or a double boiler on the stove, melt together the cream cheese and coconut oil, until you can stir them together easily.

In a large bowl, combine the pumpkin puree, melted coconut oil/cream cheese mixture, eggs and vanilla. Beat with a hand mixer at medium speed, until smooth.
In another bowl, stir together the almond flour, sweetener, baking powder, pumpkin pie spice, and salt.

Add the dry flour mixture to the wet ingredients. Beat with the hand mixer at low speed, until just combined.
Transfer the batter to the lined baking pan and smooth the top. Bake for 20-30 minutes, until an inserted toothpick comes out clean. Cool completely.
To make the frosting, use a hand mixer to beat together the cream cheese, sweetener, and vanilla, until smooth. (You can thin it out with a little milk or cream if you'd like.) Let the bars cool completely before frosting and cutting.