Preheat the oven to 350°F. Line an 8x8-inch pan with parchment paper leaving a 2-inch overhang at each side.
For the blondie batter, melt butter gently in a medium bowl in a small saucepan over low heat or in a medium heatproof bowl if using the microwave. Add both sugars and vanilla (the butter will still be slightly warm) and whisk to blend well. The mixture may look grainy and a bit separated at this point.
Add egg and whisk vigorously until well combined, smooth and glossy. Mix in salt and baking soda. Add flour and fold it in until evenly combined. Add the chocolate chips and fold them through.
For the brownie batter, melt chocolate and butter together in a small saucepan over low heat or in a medium heatproof bowl if using the microwave. Add egg, sugar and salt and whisk until smooth and glossy. Fold in flour.
Dollop big spoonfuls of brownie batter alternately with blondie batter in the prepared pan to roughly cover the bottom of the pan. Then add spoonfuls of brownie batter over the blondie batter and vise versa. Do not spread it out. Use a knife to swirl the batters together and then just tilt the pan if you need the batter to move into the corners.
Bake for 23-26 minutes until the top of the blondie batter is evenly golden brown. It should puff up in the center and then fall slightly, and it will still feel just slightly soft in the middle. Transfer pan to a wire rack and let cool completely before cutting into squares.