To make the cookies, in a medium mixing bowl, whisk together the flour, baking powder, cinnamon and salt until well combined.
In a large mixing bowl, whisk the sugar, zest and rosemary until it has the consistency of wet sand. Whisk in the olive oil and egg until smooth and well combined.
Alternate mixing the dry ingredients and buttermilk into the wet until all the dry ingredients and buttermilk have been added. Rest the cookie dough at room temperature for 30 minutes.
Preheat the oven to 375°F (190°C). Line two large baking sheets with parchment paper.
Scoop 1-tablespoon amounts of cookie dough onto the baking sheets, spacing them 2 inches apart. Bake for 9 to 11 minutes, or until a finger lightly pressed into the top of the cookie bounces back. Keep the cookies on the hot baking sheets for 3 to 4 minutes before transferring them to a cooling rack to cool to room temperature.
Blood Orange Glaze
While the cookies cool, make the glaze. In a medium mixing bowl, add the confectioners’ sugar. Whisk in the lemon juice, zest if using and 1 to 3 tablespoons of the blood orange juice, to taste. Spoon the glaze over the cooled cookies, and let it set for 30 to 45 minutes before serving.