In a small bowl, use an electric mixer to beat the softened cream cheese and sugar until smooth and free of lumps. Add the egg yolk and vanilla extract, mixing just until combined. Drop small, 1-teaspoon-sized dollops of the mixture onto a parchment-lined plate and freeze for at least 30 minutes until firm.

In a large bowl, whisk together the melted butter, brown sugar, and granulated sugar until well-combined. Whisk in the egg and egg yolk until the mixture is smooth. In a separate bowl, stir together the flour, cornstarch, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing with a spatula until just combined.

Preheat your oven to 350°F (175°C). Take a portion of cookie dough (about 1.5 tbsp) and flatten it. Place one frozen cheesecake dollop and one soft caramel in the center. Wrap the cookie dough around the fillings, rolling it into a smooth ball. Place dough balls 2-3 inches apart on a parchment-lined baking sheet.

Bake for 12-15 minutes, or until the edges are set and golden-brown and the tops have developed cracks. Let the cookies cool on the baking sheet for 10 minutes before transferring to a wire cooling rack to cool completely.