Turn the oven to 350°F (180°C). Line a baking sheet with parchment paper.
In a bowl, mix ½ cup sunflower oil with ¼ cup granulated sugar and ¾ cup brown sugar. Add 1 ½ cups pumpkin puree and mix.
Add 1 egg, ½ teaspoon vanilla extract, 1 teaspoon ground cinnamon, ½ teaspoon ground gingerpinch of ground nutmeg and pinch of ground cloves and incorporate very well.
Add the sifted dry ingredients (1 ½ cups all-purpose or cake flour, 1 ¼ teaspoon salt, ½ teaspoon baking powder and ¼ teaspoon baking soda) in 2 parts and mix without beating. You will have a soft mixture. Sift the flour mixture before or have it measured and sift it directly over the pumpkin batter, as I do.
Spoon tablespoons onto the prepared sheets, leaving an inch or two between them.
Bake for 10 to 12 minutes, until dry and puffed. Let cool on a wire rack.
Fill half the rounds with 2 teaspoons per cookie and cover with a plain round, making a sandwich. They are squishy.
Leftovers can be left covered at room temperature or refrigerated (my choice).
Beat 2 tablespoons unsalted butter and 4 tablespoons cream cheese until creamy and smooth.
Add 2 cups powdered sugar little by little until it is very thick. Add more sugar if you want a thicker mixture.