Preheat your oven to 400 degrees Fahrenheit and line two baking sheets with parchment paper or silicone baking mats to prevent sticking.
In a small bowl, whisk together pumpkin puree, brown sugar, vanilla extract, cinnamon, ginger, nutmeg, cloves, and egg until smooth and well combined.
In another bowl, beat together softened cream cheese, sugar, and vanilla extract using an electric hand mixer or stand mixer until creamy and smooth.
On a lightly floured surface, roll out the thawed puff pastry into an approximate 12" x 9" rectangle; it doesn't have to be precise but should be even enough for cutting.
Divide the pastry into four strips lengthwise then cut each strip into three equal rectangles—making twelve in total—before lightly scoring a border around each piece without piercing through.
Fill each scored rectangle with cream cheese filling followed by a layer of pumpkin mixture on top before brushing edges with egg wash; bake until golden brown (15-20 minutes), rotating halfway through baking time for even cooking.