Earl Grey and Blueberry Cake

For the infused milk :
150ml whole milk
4 Earl Grey tea bags

For the cake :
350g unsalted butter, softened
350g caster sugar
6 large eggs
350g self raising flour
1tsp baking powder
1tsp vanilla extract

For the frosting :
250g unsalted butter
450g icing sugar
1tsp vanilla extract
4tbsp milk
blueberry jam
fresh blueberries to decorate