In a medium bowl, combine the cream cheese, powdered sugar, and flour. Whisk together until smooth and creamy; this will be the luscious heart of your cookies.

Line a cookie sheet or plate with wax paper. Use a cookie scoop to drop spoonfuls (about 2 teaspoons) of the filling onto the lined sheet, then freeze for at least 2 hours.

In a medium bowl, whisk together the all-purpose flour, cocoa powder, baking soda, and salt.

In a large bowl, beat together the softened butter, brown sugar, and granulated sugar until creamy and fluffy.

Mix in the egg, vanilla extract, distilled vinegar, and red food coloring into the butter mixture.

Gently beat the dry ingredients into the wet mixture until just combined.

Cover the bowl with plastic wrap and refrigerate the dough for at least 2 hours, or up to 48 hours.

Scoop 1 to 1.5 tablespoons of cookie dough into your hands, flatten it slightly, and create a shallow bowl shape.

Retrieve a frozen cream cheese dollop from the freezer and place it on top of the cookie dough.

Scoop another 1 to 1.5 tablespoons of dough, flatten it, and cover the cream cheese filling. Pinch the edges to seal the filling and roll into a ball.

Pour the extra 1/3 cup of granulated sugar onto a plate and roll the cookie dough balls into the sugar.

Place the cookie dough balls on a lined plate and freeze for at least 30 minutes.

Preheat your oven to 350°F (180°C) and line baking sheets with parchment paper.

Place the frozen cookie dough balls on the lined sheets, ensuring they are at least 2 inches apart. Bake for about 12-14 minutes, or until the tops look set.

Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack.

For the glaze, whisk together 1 tablespoon of milk and 1 cup of powdered sugar until smooth.

Drizzle the glaze onto the cooled cookies.