In a large bowl, beat 1 cup of softened unsalted butter with 1 cup of granulated sugar and ½ cup of light brown sugar until fluffy.
Add 2 room-temperature eggs, 2 teaspoons of vanilla extract, and 1 teaspoon of maple extract. Mix until smooth.
In another bowl, combine 4 cups of cake flour, 1½ teaspoons of baking powder, ¼ teaspoon of baking soda, and ¾ teaspoon of salt.
Gradually mix this dry mixture into the wet mixture until everything is combined. Scrape the sides and bottom of the bowl. Cover the bowl and refrigerate for at least 60 minutes.
In a bowl, mix ½ cup of softened butter, ¼ cup of granulated sugar, ¼ cup of brown sugar, and 1 teaspoon of cinnamon. Stir in 1 cup of all-purpose flour and ⅛ teaspoon of salt until the mixture is crumbly.
Mix ¼ cup of softened butter with 1 cup of powdered sugar, ½ teaspoon of maple extract, and ⅛ teaspoon of salt until well combined. Shape this mixture into 17 small squares and set aside.
Preheat the oven to 350°F (175°C). Use a cookie scoop to portion 60g of dough for each cookie and roll them into balls. Flatten a tablespoon of crumble topping and press it onto each ball.
Bake for about 13 minutes, or until the edges are lightly golden.
After baking, press the cookies down with a measuring cup and shape them into squares while they are warm.
Press a butter square onto each warm cookie and let it melt slightly. Allow the cookies to cool before moving them, as they are fragile when warm.