Position a rack in the center of the oven and preheat the oven to 350 (F). Generously spray three 8-inch round cake pans with cooking spray and line the bottom of each with a parchment paper circle. Spray the parchment too.

In a large bowl, whisk together the flour, brown sugar, baking powder, baking soda, and salt. Add peanut butter, buttermilk, water, canola oil, eggs, and vanilla. Use a rubber spatula to mix the wet ingredients into the dry ingredients until just combined.

Divide evenly between the three cake pans and bake for 30 to 35 minutes, or until the top of each cake bounces back when gently pressed. A skewer inserted into the center of the cake should come out with a few crumbs attached. Cool completely in the pans on a wire rack before frosting.

Whisk together egg whites and sugar in the top pan of a double boiler (or, make your own by setting a heatproof bowl on top of a saucepan filled with an inch or two of simmering water—make sure the bottom of the bowl does not touch the water). Cook over medium-high heat, whisking intermittently, until the egg mixture registers 160 (F) on a candy thermometer.

Once hot, immediately pour into the bowl of a stand mixer fitted with the whisk attachment. Beat on high speed for 8 to 10 minutes, until the mixture is light, fluffy, and holds medium-stiff peaks. When done, the outside of the mixer bowl should be at room temperature. Scrape down the bottom and sides of the bowl, and the whisk attachment. Swap the whisk attachment for the paddle attachment.

With the mixer on low, add the butter, a few tablespoons at a time. Once incorporated, increase to medium-high and beat until the buttercream is silky smooth, 3 to 5 minutes. Scrape down the bottom and sides of the bowl. With the mixer on low, gradually add the jelly, 1 to 2 tablespoons at a time. Once incorporated, increase to medium-high and beat until silky smooth and pale pink-purple, 2 to 3 minutes more.