In a medium bowl, beat the softened cream cheese with a hand mixer on medium speed until smooth and lump-free. Add the powdered sugar and 1/2 teaspoon vanilla extract, then beat again until creamy and thick, scraping down the sides as needed. Scoop small mounds of filling, about 2 teaspoons each, onto a parchment-lined plate or tray (you should get about 14–16 portions). Chill or briefly freeze the filling portions while you prepare the cookie dough.

In a large mixing bowl, beat the softened butter, brown sugar, and granulated sugar together on medium speed for 2–3 minutes, until light and fluffy. The mixture should look slightly lighter in color and a bit airy.

Beat in the egg, egg yolk, and 1 1/2 teaspoons vanilla extract until well combined and glossy. Add about 1 tablespoon red gel food coloring and mix until the color is uniform. If the color looks too dull, add a bit more food coloring, a little at a time; the dough should be a deep red, as it will lighten slightly once the flour is added and during baking.

In a separate bowl, whisk together the flour, cocoa powder, cornstarch, baking soda, and salt until well combined.

Add the dry ingredients to the wet mixture in two additions, mixing on low speed just until no dry streaks remain. If the dough seems very stiff or crumbly, mix in 1 tablespoon of buttermilk or milk, adding up to 1 additional tablespoon only if needed to help the dough come together. The dough should be soft and thick but not sticky like cake batter. If using, gently fold in the white chocolate chips.

Cover the bowl of dough and chill it in the refrigerator for 30–45 minutes. Chilling helps the stuffed cookies hold their shape and prevents excessive spreading during baking.

Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats. Remove the chilled cream cheese filling portions from the refrigerator or freezer and have a small cookie scoop or tablespoon ready for portioning the dough.

Scoop about 2 tablespoons (around 40 g) of dough for each cookie; you should get roughly 14–16 cookies. Working one at a time, flatten a portion of dough gently in your palm into a thick disc. Place one chilled cream cheese mound in the center, then wrap the dough up and around the filling, pinching the seams closed. Roll gently into a ball so the cream cheese is completely enclosed. Place stuffed dough balls on the prepared baking sheets, spacing them about 2 inches apart. If desired, press a few extra white chocolate chips or sprinkles onto the tops for decoration. If the dough becomes too soft or sticky while shaping, briefly chill the tray in the fridge for about 10 minutes before continuing.

Bake one sheet at a time in the preheated oven for 11–13 minutes, or until the edges look set and the tops have developed crackly lines. The centers should still look slightly soft and puffy; they will firm up as they cool.

Allow the cookies to cool on the baking sheet for about 10 minutes, as they are fragile when hot due to the soft centers. Then transfer to a wire rack to cool completely. Serve slightly warm for a gooier cream cheese center, or fully cooled for a cheesecake-like texture.