Preheat the oven to 350 and prepare a bundt pan with grease. Set to the side.
Mix the flour, baking powder, baking soda, and salt in a bowl. Set to the side.
Zest the lemons and chop the rosemary. Combine the ingreidents In a meduim-sized bowl, set to the side.
Supreme the lemons. Make sure to use a sharp knife and do not get any of the white pith into the bowl, as that will make the flavor bitter. Give a rough chop to them lemons place in bowl.
Add the sugar to the zest and rosemary mixture. Use your hands to massage the sugar into the mixture. This will bring out the natural oils in the zest and rosemary.
In a bowl with a hand mixer or in a bowl of a stand mixer with a paddle attachment, cream the butter and oil with the sugar mixture, scraping down the bowl as needed. Add the eggs in one at a time, followed by the vanilla. Add in the lemons and the sour cream. Don't worry if the mixture looks slightly curdled.
Slowly add in the flour mixture, scraping down the sides as needed. The batter will be very thick.
Add the batter to the prepared bundt pan and cook in the oven for 50-60 minutes.
While the cake is cooking, make the glaze. In a medium-sized bowl, combine the powdered sugar, lemon juice, heavy cream, and vanilla in a bowl. Mix until desired texture is reached.
Let the cake fully cool before removing it from the bundt pan. When the cake is cool, remove it from the pan and add the glaze on top.
