In a saucepan, put the chopped strawberries and raspberries, add balsamic vinegar, cane sugar, and arrowroot powder. Stir well and bring to a light boil. Cook on low heat for a few minutes until the fruit starts to melt and the mixture thickens, stirring from time to time. Set aside.
To make the Brownies:
Preheat oven to 325 F. In an 8-inch square baking dish, line two strips of parchment paper, leaving a 2-inch overhang on two sides; butter the parchment (I did not do it and the brownie really did not stick).
In a heatproof bowl set over a pot of simmering water, melt chocolate and butter until smooth. Let it cool slightly (must be warm but not hot). With a hand mixer, beat in the sugar and the vanilla until well incorporated. Add the two eggs and whisk until the mixture is glossy and smooth. Using a rubber spatula to stir in the flour until well combined.
Pour the batter into the prepared baking dish, spreading it evenly with a rubber spatula. Evenly spoon the jam in dollops over the batter, then swirl gently with a toothpick or knife to create a marble effect.
Bake for about 30-35 minutes or until a toothpick inserted in the center comes out almost clean. Do not overcook them (the edges should look cooked and the center slightly wet).
Transfer the pan to a wire rack and let the brownies completely cool in the pan.
Remove brownies from pan, using parchment handles.
Using a sharp knife (*), cut the brownies into 16 squares (4 x 4).
(*) To have a clean cut of brownies, dip between each cutting your knife blade in hot water and wipe your blade if necessary.