Zest and juice one lemon, keeping each in a separate bowl. Measure the powdered sugar into a small bowl and set it aside. In another bowl, measure the flour, baking powder, and salt, then whisk to combine. Finely dice the rosemary so it blends smoothly into the dough and enhances the lemon and honey without overpowering them.
Cube the butter into a mixer bowl and on a medium mixer speed cream the butter until it has soft looking peaks (about a minute). Reduce the mixer speed to low and gradually add the powdered sugar. Once incorporated, increase the speed back to medium and mix for about 3 minutes. Scrape down the sides of the bowl, then mix for another thirty seconds.
Add the lemon zest, lemon juice, honey, and diced rosemary, mixing until evenly combined. Turn the mixer to low and add about a third of the flour mixture at a time. Mix just until incorporated. Turn off the mixer, scrape down the sides of the bowl, then mix for another thirty seconds.
Remove the bowl from the mixer and scrape the cookie dough onto a pastry mat lightly dusted with powdered sugar. If you have a pan long enough to cradle a single log, you can keep the dough whole. Otherwise, divide the dough in half and shape it into two logs, each about eight inches long and two and a half inches in diameter.
Cut a piece of plastic wrap longer than each log so the ends can be folded underneath. Roll each log tightly in the plastic wrap, then repeat with the second log. I use a baguette pan to cradle my logs while they are in the fridge chilling. Chill for at least 1 hour. Chilling the dough firms it up, which makes slicing the logs much easier.
A helpful trick I learned from another baker is to use the cardboard center from a paper towel roll. Cut the roll in half lengthwise, then place the plastic-wrapped log into one of the halves. The cardboard helps the dough keep its round shape, giving you evenly shaped cookies. Place both logs on a sheet pan and refrigerate for at least 1 hour.
Preheat the oven to 350°F (175°C or 180°C) and line a cookie sheet with parchment paper. Remove one cookie log from the refrigerator and unwrap it. Place the log on a cutting board and slice the dough into cookies about ½" to ⅝". Arrange all the slices from one log onto a single cookie sheet and bake for 10 to 12 minutes, until the cookies are lightly golden along the bottom edges. Leave the cookies on the sheet pan for about one minute after removing them from the oven, then gently transfer them to a cooling rack to finish setting.