Preheat the oven:
Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan or line it with parchment paper.

Prepare the dry ingredients:
In a medium bowl, whisk together the all-purpose flour, baking powder, and kosher salt. Set aside.

Mix wet ingredients:
In a large bowl, mix the sugar and melted butter until smooth. Add the egg, egg yolk, and vanilla extract. Stir until fully combined.

Add dry ingredients:
Gradually add the dry ingredients to the wet mixture and mix until just combined.

Incorporate freeze-dried strawberries:
Grind the freeze-dried strawberries into a fine powder using a food processor or blender. Gently fold this powder into the batter.

Bake the cake:
Pour the batter into the prepared cake pan and spread it out evenly. Bake in the preheated oven for 30-35 minutes or until a toothpick inserted into the center comes out clean. Let the cake cool completely in the pan before removing it.

Prepare the strawberry filling:
While the cake is cooling, beat the softened cream cheese until smooth and fluffy. Gradually add powdered sugar, and continue mixing until fully combined. Add the egg and strawberry preserves, and beat until smooth. Finally, fold in the freeze-dried strawberries.

Assemble the cake:
Once the cake is completely cooled, slice it into two even layers. Spread the strawberry filling evenly on the bottom layer, then place the second layer on top.

Serve and enjoy:
Optionally, you can frost the cake with extra strawberry preserves or whipped cream for a decorative touch. Slice and serve!