Preheat the oven to 350ºF. Line an 8 × 8-inch baking pan with parchment paper, leaving about 2 inches of overhang on each side. Coat lightly with cooking spray.
Place the dates in a medium bowl. Cover the dates with the hot water. Set aside until the dates are softened, about 10 minutes. Drain the dates, reserving A cup of the soaking liquid. Combine the dates and the reserved soaking liquid in a food processor fitted with a metal blade. Process until smooth, about 1 minute. Set aside.
Combine the butter and chocolate chips in a large heatproof bowl, set over a saucepan filled with 1 inch of simmering water, making sure the bottom of the bowl doesn’t touch the water. Stir until melted. Remove from the heat and let cool slightly. Whisk in the sugar, vanilla, and eggs. Add the date puree and stir until combined. Add the flour, cocoa powder, salt, and baking powder and stir until combined.
Transfer the batter to the prepared pan, spread in an even layer, and bake until the top is set and a toothpick inserted into the center comes out clean, 15 to 20 minutes. Let the cake cool completely.
Meanwhile, make the frosting: Beat the butter on medium speed in the bowl of a stand mixer fitted with a paddle attachment until smooth, about 2 minutes. Add the peanut butter and continue to beat until fully combined, about 1 minute, scraping down the side of the bowl as needed. Add the sugar, vanilla, and salt and mix until just combined.
Spread the frosting on the completely cooled cake and cut into 16 squares.