Preheat your oven to 350°F (175°C). Grease and flour a 9x13-inch baking dish or line it with parchment paper.
Mix the cake mix, vanilla pudding mix, eggs, oil, milk, vanilla extract, and softened cream cheese in a large bowl. Beat with a hand mixer on medium speed for 2–3 minutes until smooth. Gently fold in the diced strawberries.
Beat the cream cheese, sugar, egg yolk, and vanilla extract in a separate bowl until smooth and slightly thickened.
Pour the cake batter into the prepared pan. Drop spoonfuls of the cream cheese mixture on top and swirl it into the batter with a knife.
Mix flour and sugar in a small bowl. Add cold butter cubes and use a fork or pastry cutter to work the butter into the dry ingredients until coarse crumbs form. Stir in freeze-dried strawberries, if using.
Sprinkle the crumble topping over the cake batter. Bake for 35–40 minutes, or until a toothpick inserted comes out clean and the topping is golden.
Let the cake cool for at least 20 minutes before slicing. Serve slightly warm or at room temperature.