In a mixing bowl, combine ¾ cup of softened cream cheese with ¼ cup of powdered sugar. Use a hand mixer on medium speed until smooth and creamy, about 2 minutes. Scoop the filling into small mounds (about 1 tablespoon each) onto a parchment-lined baking sheet. Freeze for 30 minutes until firm.

In a large bowl, cream together 1 cup of softened butter, ¾ cup of white sugar, and ¼ cup of brown sugar until light and fluffy, about 4 minutes. Beat in 1 large egg, 1 egg yolk, and 1 teaspoon of vanilla extract until well combined.

In a separate bowl, whisk together 2¾ cups of all-purpose flour, 1 teaspoon of baking soda, and ¼ teaspoon of salt. Gradually add this dry mixture to the wet ingredients, stirring gently until combined.

Fold in ½ to ⅔ cup of diced fresh strawberries into the cookie dough, being careful not to overmix. Cover the bowl with plastic wrap and refrigerate the dough for 30 to 60 minutes.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Scoop about 1 tablespoon of the chilled dough, flatten it in your palm, and place a frozen cheesecake filling mound in the center. Encase the filling by folding the dough over it, rolling it into a ball.

Place the stuffed cookies on the prepared baking sheet about 2 inches apart. Bake for 12 to 14 minutes or until the edges are lightly golden.