Preheat oven to 350 degrees. Grease a 12-count muffin tin, then line it with cupcake papers.
To a stand mixer fitted with the paddle attachment, add the softened butter, oil, and sugar, and beat until light and fluffy, about 2 minutes. Gradually add the eggs, zest, blood orange juice, and rosemary, scraping the sides of the bowl as needed.
In a mixing bowl, stir together the flour, cornmeal, baking powder, and salt. With the mixer on low, steadily add the cornmeal and flour mixture to the wet ingredients, mixing until everything is well combined, scraping the bottom and sides of the bowl as you go. Divide the batter evenly into the twelve muffin cups (I use a medium cookie scoop for this). Place a thin slice of blood orange on top of each muffin. Bake for 22-24 minutes, until cooked through in the center and golden on the edges. Remove to a cooling rack to cool.
To make the glaze: whisk together the blood orange juice and powdered sugar until smooth. Spoon a generous amount of the glaze over the top of each muffin. Allow the glaze to set about ten minutes before serving.