Preheat the oven to 350°F (175°C). Grease a cake pan.
In a bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, beat sugar and butter until fluffy. Add eggs, pumpkin, and vanilla. Mix until combined.
Gradually add the dry ingredients to the wet mixture, stirring until smooth.
For the cream cheese filling: Beat cream cheese, sugar, vanilla, and egg until smooth.
Pour half the cake batter into the pan. Add a layer of cream cheese filling. Top with remaining batter.
For the streusel: Mix sugar, flour, and cinnamon. Add butter until crumbs form. Sprinkle over the cake.
Bake for 40-45 minutes, or until a toothpick comes out clean.
Cool for 10 minutes, then transfer to a cooling rack.