Step 1: Preheat your oven to 350°F (175°C). Grease and flour a 9×13 inch baking pan. Set aside.
Step 2: In a large bowl, whisk together the all-purpose flour, granulated sugar, light brown sugar, baking soda, ground cinnamon, ground ginger, ground nutmeg, and salt until well combined.
Step 3: In a separate medium bowl, whisk together the pumpkin puree, vegetable oil, eggs, and vanilla extract until smooth.
Step 4: Pour the wet ingredients into the dry ingredients. Mix with a spatula or wooden spoon until just combined. Be careful not to overmix.
Step 5: Pour the batter evenly into the prepared baking pan. Bake for 25-30 minutes, or until a wooden skewer inserted into the center comes out clean. Let the cake cool completely in the pan on a wire rack.
Step 6: While the cake cools, prepare the caramel icing. In a medium saucepan, combine the unsalted butter, dark brown sugar, and sweetened condensed milk. Place the saucepan over medium heat, stirring constantly until the butter is melted and the sugar is dissolved.
Step 7: Bring the mixture to a gentle boil, then reduce the heat to low and continue to cook for 5 minutes, stirring occasionally.
Step 8: Remove the saucepan from the heat and stir in the vanilla extract. Let the caramel cool for about 10-15 minutes, stirring occasionally, until it thickens slightly but is still pourable.
Step 9: Once the cake is completely cool, pour the slightly warm caramel icing evenly over the top. Use an offset spatula to spread it to the edges. Allow the icing to set slightly at room temperature or in the refrigerator before slicing and serving.