Preheat your oven to 350°F. Line an 8 by 8-inch baking pan with foil or parchment paper, making sure to leave an overhang on the sides. This makes lifting out the bars much easier after baking.

In a medium microwave-safe bowl, microwave 1 stick (4 oz) unsalted butter until melted. Let it cool until just warm, about 80°F, to avoid scrambling the egg later. Once cooled, whisk in 2/3 cup packed light brown sugar, 1 large egg (at room temperature), 1 teaspoon vanilla extract, and 1 cup pumpkin puree until everything is fully combined.

In a large bowl, whisk together the dry ingredients: 1 1/2 cups all-purpose flour, 1 teaspoon ground cinnamon, 1/4 teaspoon ground ginger, 1/4 teaspoon ground nutmeg, 1/4 teaspoon baking soda, and 1/4 teaspoon fine sea salt. Make sure everything is well distributed for an even flavor.

Add the wet mixture from Step 2 to the bowl of dry ingredients from Step 3. Stir until just combined; the batter will be thick. Spread the batter evenly in the prepared baking pan with a spatula. Bake for 25 minutes, or until a cake tester inserted in the center comes out clean. Be careful not to overbake, as this can dry out the bars. Set the pan on a wire rack and allow the bars to cool completely in the pan.

In a large bowl, use an electric mixer on medium-high speed to beat 1 stick (4 oz) unsalted butter (at room temperature) and 1/4 cup packed light brown sugar until the mixture is light, fluffy, and smooth. Scrape down the bottom and sides of the bowl. Add 1/2 teaspoon ground cinnamon and 1/8 teaspoon fine sea salt, mixing to combine. On low speed, slowly add 1 1/2 cups sifted powdered sugar until incorporated. Add 1/2 teaspoon vanilla extract and 1 tablespoon milk, then beat on medium-high speed until the frosting is very light and fluffy, about 2–3 minutes. If too runny, add a bit more powdered sugar; if too thick, add a splash more milk. I like to taste and adjust the milk and powdered sugar to get just the right creamy texture.

Once the pumpkin bars have cooled completely in the pan (from Step 4), spread the fluffy cinnamon frosting (from Step 5) evenly over the top. Use the overhang to lift the bars from the pan, cut them into squares, and serve. Store in an airtight container at room temperature for up to 1 day, or in the fridge for up to 5 days.