Pumpkin cake with pumpkin frosting 
recipe by vanillasugarblog.com

pumpkin cake:
1 cup unsalted butter, softened + more for greasing pan
1 ½ cups sugar
3 Tb pumpkin butter
1 1/2 cups all-purpose flour, plus more for pans
1 1/2 cups cake flour (not self-rising)
¾ TB baking powder
¾ ts salt
4 large eggs
1 cup whole milk

pumpkin buttercream:
2 sticks unsalted butter, softened
¾ of a 1lb bag powdered sugar
3-4 TB pumpkin butter
giant pinch of sea salt
1-2 TB half & half (or whole milk)
¼ -1/2 cup chopped walnuts or pecans, for garnish (optional)

Preheat oven to 350 degrees.

Butter a 9 x 13 pan; line the bottom with parchment paper and/or grease up with butter. 
If you use parchment, make sure to butter that as well.

Into a medium bowl, sift together the flours, baking powder, and salt; set aside. 
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and sugar until well combined, then add in the pumpkin butter. 
Add in the eggs, one at a time until all is well combined.
Take your flour mixture and beat it in in 3 parts, alternating with three parts of the milk. 
So add in one third of flour mixture, mix, then add in one third of the milk and mix. Then repeat.
I had a couple of lumps left in batter, so that’s ok. I hate to overbeat the batter.

Pour batter into prepared pan.
Bake about 22-28 minutes. It does bake up fast, so make sure to check at the 23 minute mark.
Let this cake cool completely before frosting.
To make the frosting, using an electric mixer, mix all ingredients, adding in 1 tablespoon at a time the half & half. 
You may not need the 2 TB of half & half, so just add in 1 TB at a time.
When cake is cooled, add on the frosting, then garnish with chopped walnuts or pecans. 
I have no idea how long this cake lasts as it was gone in one day in my house. 
But I bet it would do well for a couple days, if nice and covered.