Line an 8×8-inch baking pan with parchment paper and preheat the oven to 350 degrees Fahrenheit (175 degrees Celsius).
In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and allspice.
In a separate bowl, whisk the melted butter, brown sugar, and eggs until smooth. Whisk in the Greek yogurt and vanilla.
Add the dry ingredients to the wet ingredients and stir just until combined. Fold in the chopped apples.
Pour the batter into the prepared pan and smooth the top. Bake for 35 – 40 minutes, or until a toothpick or cake tester inserted in the center comes out clean. Let the cake cool in the pan for 30 minutes.
To make the optional caramel glaze, combine the butter, brown sugar, cream, salt, and vanilla in a small saucepan over medium heat. Stir frequently until the sugar is dissolved and the mixture is gently bubbling. Remove from the heat and cool for a few minutes.
Pour the glaze evenly over the cooled cake and allow it to set and cool for 15 minutes then cut into 16 squares, and serve.
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Notes
You can use any type of apple, but I like to mix sweet, fresh apples like Honeycrisp with tart apples like Granny Smith for a delicious apple flavor.
Check for doneness early. Ovens vary, so start checking at 32 minutes. The toothpick should come out clean or with just a few moist crumbs.
Make-ahead: Bake the cake a day ahead and add the glaze just before serving to keep it looking fresh.
Chopped pecans would be a great addition to this cake if you like a crunch!