Put the softened butter and honey into a bowl of an electric mixer fitted with a paddle, and gradually work it into a soft paste. This could also be done by hand.
Sift the almond flour and arrowroot starch into the creamed butter and honey mixture. Gently mix again on low, until a crumbly, soft dough forms. Fold in the finely minced rosemary. Using your hands, knead the dough together to form a ball, then flatten into a disc and place between two sheets of parchment paper or in plastic wrap and place into the fridge. Chill until the dough is more firm, at least 30 minutes, up to 2 days.
Preheat the oven to 325ºF and line a baking sheet with parchment paper. Place the disc of dough between two sheets of parchment paper lightly sprinkled with arrowroot starch sprinkling a little on top of the dough,as well. Using a rolling pin, roll the dough out to around 1/4-inch thick. Lightly dust the cookie cutter you plan to use (I used a 2-inch fluted circle) with a little arrowroot starch as well. Remove the top parchment paper and begin cutting out the cookies. You could also cut them into bars.
Carefully transfer the cookies to the parchment lined baking sheet, about 1 to 1 1/2-inches apart. I find using a metal spatula dusted with a little arrowroots, to transfer, to be easiest. Reroll dough scraps to 1/4-inch thickness and cut out additional cookies. You may need a couple baking sheets. Bake for 12-15 minutes until ever so slightly golden brown. Watch them carefully so they don't brown too much.
Allow the cookies to cool slightly on the pan, before transferring to a cooling rack to cool completely.
Once cooled, melt your chocolate using the double boiler method (a bowl over a pan with simmering water) or in small increments in the microwave. Stir vigorously until the chocolate is smooth and slightly cooled; stirring makes it glossier.
Dip half of each cookie into the melted chocolate and transfer to parchment or wax paper to cool. Once cooled, store in air-tight container or bag in the fridge.
Notes
The dough can keep in the refrigerator up to 2 days ahead. You can also roll the dough into a 2-3 inch log before refrigerating and simply slice the log into 1/4-inch thick discs, instead of rolling it out. Baking time can vary slightly depending on how powerful your oven is, so keep a watchful eye on your cookies, you want them ever so golden, definitely not browned. To make vegan opt for maple syrup and coconut oil or palm oil shortening and use vegan chocolate