Preheat oven to 180C/160C fan/350F. Lightly grease and line 2 6" loose-bottomed baking tins (or 4 if you have them).
Place your room temperature brown butter in the bowl of your stand mixer (or use a large mixing bowl and a hand mixer). Add the sugar and cream together with the paddle attachment for a few minutes until pale and fluffy.
225 g (1 cup) browned unsalted butter, at room temp, 225 g (1 cup) caster sugar
In another bowl, whisk together the flour, baking powder and salt.
225 g (1 ½ cups) plain flour, 2 teaspoons baking powder, ¾ teaspoon fine sea salt
Crack in the eggs one at a time, adding a tablespoon of the flour mixture with each one to prevent curdling, beating well for a minute or two between each egg.
4 large eggs
Add all but one tablespoon of the flour to the butter/egg mixture. With the mixer on low, slowly mix in the flour until combined.
Pour in the milk and vanilla extract and mix gently until combined. Do not overbeat the mixture.
60 ml (¼ cup) milk, 2 teaspoons vanilla extract
Toss the chocolate chips with the remaining flour and then gently fold these into the batter.
175 g (1 cup) chocolate chips
Divide the batter evenly between the 2 (or 4) tins. If using 2 tins, keep the other half of the batter at room temperature until the other cakes have come out of the tins. Place in the oven and bake for about 20 minutes until golden and an inserted skewer comes out clean. Leave to cool in the tins for 5 minutes before turning out onto a cooling rack to cool completely. Repeat for the remaining batter if you have it.