In a large bowl, use a hand mixer to beat the room temperature butter and sugar until fluffy.
Add the eggs, one at a time, and mix until fully incorporated. Then gradually add the flour and mix until combined.
Add the juice of half a lemon and 1 tsp lemon zest. Mix using a spatula until smooth.
Scoop the mixture into a butter-greased bundt pan, spread it evenly, and bake at 350°F (180°C) for 30-40 minutes or until golden brown.
To make the lemon icing, stir together powdered sugar and the juice of half a lemon until smooth.
Once the cake is out of the oven and cooled, pour the lemon icing over the top. Garnish with lemon zest, lemon slices and rosemary stems.