With a rack at the center position, preheat the oven to 350°F. Line a 9-inch square baking dish with parchment paper and set it aside.

In a medium mixing bowl, whisk together the flour, old-fashioned oats, allspice, baking powder, baking soda, and table salt for about 30 seconds until well-combined. Set aside.

In a large mixing bowl, whisk together the melted butter, light brown sugar, and white sugar (labeled “for dough”) until a paste begins to form, about 1 minute. It won’t emulsify, but the sugar will distribute through the butter and thicken the mixture. Add the eggs and vanilla paste, or vanilla extract, and whisk for another minute.

Immediately toss the chopped green apples in the dry ingredients until all pieces are coated. Then, add that mixture to the large mixing bowl with the wet ingredients. Use a silicone spatula or wooden spoon to combine everything until there’s no more visible flour. Drop the dough by spoonful into the parchment-lined square baking dish — adding it by spoonful helps keep the parchment paper in place. Use an offset spatula to completely smooth the top of the dough in the pan, and sprinkle the white granulated sugar (labeled “for topping”) evenly over the top.

Bake in the preheated oven for 35 minutes. Once it’s done, allow it to cool for about 15 minutes before transferring to a board for slicing. It’s best enjoyed immediately with vanilla ice cream and caramel.