Heat oven to 350°F (180°C). Place white chocolate bars on a light-colored baking sheet lined with parchment paper or a silicone baking mat. Bake for 15–20 minutes until the chocolate is golden brown and caramelized. Allow chocolate to cool, but keep the oven heated. Crumble caramelized white chocolate and set aside.
Whisk together flour, cornstarch, baking soda, and fine sea salt in a mixing bowl.
Add butter, brown sugar, and granulated sugar to a large bowl or stand mixer fitted with a paddle attachment. Beat together on medium speed for 2 minutes using a handheld electric or stand mixer until the mixture is light and fluffy. Add in eggs and vanilla extract, and beat on medium speed until combined.
Scrape down the side of the bowl, then add the flour mixture, and mix on low speed just until combined. The dough will be thick.
Mix crumbled caramelized white chocolate into the dough by hand with a silicone spatula.
Scoop 2 tablespoons (40 grams) of dough onto a parchment-lined light-colored baking sheet spaced 3 inches (8 cm) apart. Bake for 14–17 minutes at 350°F (180°C) until cookies are golden brown. Transfer to a wire cooling rack until cool to the touch.
Store cookies in an airtight container at room temperature for up to 7 days.