Preheat the Oven:
Preheat your oven to 350°F (175°C). Lightly spray an 8×8 or 9×9 inch baking dish with non-stick spray.
Mix Dry Ingredients:
In a medium bowl, whisk together the flours, salt, baking powder, baking soda, cinnamon, nutmeg, cloves, and ginger.
Prepare Wet Ingredients:
In a large bowl, mix the egg and sugars until combined. Whisk in Greek yogurt and vanilla extract, then stir in the pumpkin puree until smooth.
Combine Batter:
Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Bake the Base Layer:
Spread half of the batter into the prepared baking dish and bake for 10 minutes. Remove from the oven.
Make the Caramel Sauce:
In a small saucepan, stir together brown sugar and half & half. Bring to a boil over medium heat, stirring constantly until the mixture darkens and sugar dissolves (about 4 minutes). Remove from heat and stir in butter and sea salt until smooth. Stir for 2 more minutes to cool slightly.
Add Caramel Layer:
Pour the caramel over the partially baked cake, spreading it evenly. Stir milk into the remaining batter and pour it over the caramel layer.
Finish Baking:
Bake the cake for another 20-25 minutes, or until a toothpick inserted in the center comes out clean. Remove the cake from the oven and let it cool on a wire rack.
Prepare the Glaze:
While the cake cools, make the glaze. In a small saucepan, stir together brown sugar and half & half. Bring to a boil, stirring constantly, until the mixture darkens (about 4-5 minutes). Reduce heat to low, stir in butter, and then whisk in confectioner’s sugar until smooth.
Glaze the Cake:
Pour the glaze over the cooled cake and spread it evenly. Sprinkle with coarse sea salt for a final touch. Let the glaze set before slicing and serving.