Put butter and chocolate in a small pan and melt gently on a low heat, stirring constantly. Alternatively, put butter and chocolate in a heatproof bowl placed over a pan with simmering water (bain-marie). Make sure the bowl doesn't touch the water. Let the chocolate and butter melt slowly giving it a gentle stir from time to time with silicone spatula. Once melted, remove from the heat and set aside to cool slightly.
Preheat the oven to 160C/320F/Gas Mark 3.
Whisk the eggs together with sugar and vanilla extract using hand held mixer, standing mixer with baloon whisk attachment or hand held whisk until slightly foamy and light.
Sieve flour and cocoa powder directly onto egg and sugar mixture and mix in gently again using mixer or balloon whisk. Add cooled butter and chocolate mixture and give it one last mix until incorporated.
Pour onto baking tray (roughly 24cm/8inch square) lightly buttered and lined with baking paper with two sides overlapping for easier removal of brownies later.
Put strawberry halves gently on top of the brownie mixture (cut side down) and push them in only slightly.
Bake in preheated oven for approx. 45 min until you see the papery crust form on top and batter no longer wobbles when you move the pan. Also the toothpick inserted into centre should have no raw brownie batter on it.
Let the brownies cool completely in the tin and if you have lots of self restrain, pop cooled brownies in the fridge for couple of hours after. It will be much easier to slice. Bring to room temperature before serving.