Preheat your oven to 350F. Lightly grease a 9x13 inch pan then line with parchment paper with a slight overhang on each side. Grease the parchment paper as well. Set aside.
Mascarpone Cheese Mixture
Using a handheld mixer or a stand mixer fitted with the paddle attachment, beat mascarpone cheese and ½ cup sugar on medium speed until smooth and creamy (about 2 minutes). Scrape the sides of your bowl.
Add the egg and 1 tsp vanilla extract and continue to beat until incorporated. Set aside.
In a large bowl, whisk ¾ cup cocoa powder and ½ tsp baking soda until combined.
Add ⅔ cup melted butter to your chocolate mixture and whisk until thick and smooth.
Add ½ cup espresso and continue whisking until smooth and incorporated. At this point, it would seem like the espresso doesn't want to incorporate into the batter. Keep whisking and it will come together.
Add the rest of your ingredients (except the flour) and whisk until fully incorporated.
Finally, add 1⅓ cups flour and gently fold until just combined. Do not over mix.
Transfer your brownie batter into your prepared pan and spread evenly.
Top with your mascarpone mixture and try to spread around
Run a knife through the batter to create swirls and help further even out the cheese throughout the pan.
Gently tap the pan on your counter a few times to help the batter settle in.
Bake the brownies for 30-45 minutes or until it's starting to brown at the edges but the centre still feels a little jiggly (but not soupy). You want a toothpick inserted in the middle to come out with minimal but slightly moist crumbs.
Take out of the oven and allow to cool on the counter. Then chill 2-3 hours (or overnight) until the brownies are set. You can serve the brownies chilled or at room temperature.
The yield depends on how big or small you slice your brownies. These are very rich so a little goes a long way.
I've found that not all mascarpone are the same. Some are milder than others. When making your mascarpone mixture, taste it before adding the egg and decide if you need to add more sugar. Do so a teaspoon at a time; don't add more than ¼ cup.
Remember that it's better to under-bake than over-bake brownies. They will continue to cook as they cool in the pan.