Line a baking sheet with parchment paper. First make the cream cheese filling. In a small bowl, mix together the cream cheese with the powdered sugar. The softer the cream cheese, the easier it will be to combine.
Spoon 10 to 12 heaping teaspoons of the cream cheese mixture onto the parchment paper. Freeze until almost completely firm. Meanwhile, line two more baking sheets with parchment paper.
In a bowl, beat the butter, brown sugar and white sugar together until light and fluff, about 1 to 2 minutes. You can use a hand mixer or standing mixer for this. Add in the egg, egg yolk and vanilla extract.
Pour in the flour, salt, and baking soda until it’s just combined, but be sure not to over mix. Dice your strawberries, and gently fold them in.
Spoon 12 heaping tablespoons of dough onto each baking sheet. Use a spoon to press an indent into the dough. Remove the cream cheese from the freezer, and place them on the cookies of one baking sheet. Take the dough balls on the other baking sheet, and place them on top so the cream cheese is inside.
Place the cookies in the refrigerator while you preheat the oven to 180 degrees Celsius. Once heated, place the baking sheet inside and bake for 13 to 17 minutes. Once edges are slightly golden, remove from the oven and let cool for 10 to 15 minutes.