Preheat your oven to 350 and line baking sheets with parchment paper. In a small sauce pan on medium heat, brown the butter until there are golden flakes in the bottom of the pan, then pour into a mixer bowl.
Whip the butter with a paddle attachment along with the vanilla, mascarpone and both sugars until smooth and fluffy, scraping the bowl as needed.
Add the egg and blend on medium high until it is again light in color and fluffy.
In another bowl, whisk together the flour, cornstarch, baking soda and salt. Add to the mixer and mix until just combined. Add in the chocolate chunks and mix until combined.
Using a medium cookie scoop, scoop out balls of dough (I did 9 per sheet) and round them gently with your hands.
Bake for 5 minutes, then rotate cookie sheet and bake another 3-4 minutes or so until they are set on top and just lightly browning on the edges. The chocolate chunks will melt, so allow the cookies to cook fully on the sheet before moving them a cooling rack. Store at room temp or in the freezer.