This recipe makes 12 LARGE cookies. See NOTES below for instructions to make smaller cookies** Line a small baking sheet or plate with parchment paper. In a small bowl, use a whisk or mixer (depending how hard your cream cheese is) to mix the cream cheese with powdered sugar until smooth and combined.
Place 10-12 heaping teaspoons of cream cheese on the baking sheet or plate. Freeze for at least one hour, or until frozen almost completely solid.
When the cream cheese is frozen almost solid, line two large baking sheets with parchment paper and set aside. Whisk together flour, salt, and baking soda then set aside. In the bowl of a handheld mixer or standing mixer, beat the butter and sugars together until light and fluffy (about 1-2 minutes). Mix in the egg, egg yolk, and vanilla extract.
Add in the flour, salt, and baking soda, and mix until just combined (don't over-mix).
Dice the strawberries and gently fold them in. You don't want to mix them in too much or they'll get squished and the color will bleed into the dough.
Scoop 12 heaping tablespoons of dough onto each baking sheet. They should be fairly big - if measured they'd be almost 2 tbsp-sized (these are big cookies!). Press the back of a teaspoon slightly into the top of half the balls of dough to create an indent.
Remove the cream cheese filling from the freezer and place one into each of the cookies. Take a second ball of dough and place it over the cream cheese, pinching the sides to seal the cream cheese inside (see picture in post above), but making sure to not squish the cream cheese into the cookie dough. The dough may start to get sticky and a bit crumbly, and a bit harder to work with because of the strawberries, but just go with it! Wipe your hands clean before moving on to the next cookie. You should have tall balls of dough.
Refrigerate the prepared cookie dough balls and repeat with the second cookie sheet and remaining dough. Preheat the oven to 350°F and leave the cookie dough in the fridge while it preheats.
Bake the cookies in the preheated oven one sheet at a time for 13-17 minutes, or until the edges are slightly golden brown and the tops are set. Remove from the oven and leave them on the baking sheet for 10-15 minutes, then transfer to a cooling rack to cool completely.