Whisk together the flour, baking powder and salt in a bowl and set aside.

Beat the butter and sugar with an electric mixer until combined, then add the eggs and mix until combined. Reduce the speed to low and add the flour, mixing until fully combined. Then add the milk and vanilla and continue beating until just incorporated.

Spray a regular-sized doughnut pan with cooking spray. Place the batter in a piping bag fitted with a round tip and fill the pan with the batter. Bake at 350F for 10 minutes. Cool in the pan for 10 minutes, then transfer to a wire rack.

Combine 1 tbsp sugar and 1 tbsp water in a small dish and brush onto half of the doughnuts. Sprinkle sesame seeds on top.

Beat the butter and cream cheese with an electric mixer until pale and creamy. Add the confectioner’s sugar 1 cup at a time. Add the salt, milk and vanilla and beat until fluffy.

Flip the doughnuts without the sesame seeds over and spread some cream cheese frosting onto the flat surface. Top with a doughnut with sesame seeds and enjoy!