Preheat oven to 350°F. Line three baking sheets with parchment paper. Set aside.
To the bowl of a stand mixer with a paddle attachment, add butter, cream cheese, brown sugar, and confectioners' sugar. Beat on high for 2-3 minutes, or until ingredients are fully combined. Scrape down the sides of the bowl as needed.
With the mixer on low, add the egg and vanilla. Mix for about 1 minute.
Add the flour, cornstarch, baking soda, and salt. Mix on low for about 1 minute, or until ingredients are fully incorporated. Add the white chocolate chips.
Mix in the raspberries, reserving about ¼ cup for the tops of the cookies. Work quickly to prevent excessive thawing.
Using a 3-tablespoon cookie scoop, drop the dough onto the lined baking sheets, leaving about 2 inches of space between each cookie.
If needed, crumble the reserved frozen raspberries, evenly sprinkling over the tops of each cookie. Using your hand, slightly flatten each cookie.
Bake for 12-13 minutes, or until they are just slightly brown on the edges.
Allow cookies to cool for 5-10 minutes before carefully moving to a cooling rack.