Place 1 1/2 sticks of the unsalted butter in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Place the remaining 1 stick unsalted butter and 8 ounces cream cheese in a large bowl. Let everything sit at room temperature until softened, about 1 hour.
Arrange a rack in the middle of the oven and heat the oven to 350°F. Coat a 9-by-13-inch baking pan with cooking spray. Line with a parchment paper sling, leaving a 2-inch overhang on the long sides. Coat parchment paper with cooking spray.
Place 1 3/4 cups all-purpose flour, 3/4 teaspoon baking powder, 1/2 teaspoon kosher salt, 1/4 teaspoon baking soda, and 1/4 teaspoon ground cinnamon in a large bowl and whisk to combine.
Add 1 cup granulated sugar and 1/3 cup packed light brown sugar to the bowl with the 1 1/2 sticks unsalted butter. Beat with the paddle attachment on high speed until light and fluffy, about 5 minutes. Scrape down the sides of the bowl. Beat in 3 large eggs one at a time, beating each addition until combined before adding the next.
Add 2/3 cup of the creamy peanut butter and 2 teaspoons vanilla extract, and beat on medium speed until combined, about 30 seconds. Add the flour mixture and 1/2 cup sour cream and beat on the lowest until just combined, about 1 minute. Transfer the batter to the baking pan and spread out into an even layer, going all the way to the edges of the pan.
Bake until a tester inserted into the center of the cake comes out clean, 30 to 34 minutes. Let the cake cool in the pan on a wire rack.
Add the remaining 1 1/3 cups creamy peanut butter and 2 cups powdered sugar to the bowl with the butter and cream cheese. Beat with an electric hand mixer on medium speed until smooth and fluffy, about 3 minutes. (Alternatively, clean and dry the bowl and paddle of the stand mixer and beat in there instead.)
Grasping the parchment, lift the cake slab onto a serving platter. Remove and discard parchment. Spread the frosting all over the top of the cake.
Coarsely chop 1/2 cup cocktail peanuts by hand. (Alternatively, place the peanuts in a plastic zip-top bag and seal the bag. Roll a rolling pin over the peanuts until coarsely crushed.) Sprinkle the peanuts around the border of the frosted cake before slicing and serving.