Coat the inside of a slow cooker with cooking spray.
Whisk flour, brown sugar, baking powder, and baking soda together in a bowl. Whisk peanut butter, sour cream, melted butter, almond extract, and 2 tablespoons boiling water in a separate bowl until smooth. Stir flour mixture into peanut butter mixture to make a very thick batter. Scoop batter into prepared slow cooker.
Whisk white sugar, cocoa powder, and 2 cups of boiling water in a bowl until thoroughly combined. Pour chocolate mixture over batter in slow cooker.
Cook on High until cake begins to pull away from the sides of the cooker and feels firm on top, about 1 1/2 hours. Allow to cool 15 minutes before serving. Drizzle with chocolate syrup.