Measure out all ingredients and prepare them before mixing. Finely chop the rhubarb into 1/4-inch pieces and set aside. Sift the powdered sugar to remove lumps for the frosting, and zest the lemon. In a small bowl, whisk together the flour, baking soda, salt, and cinnamon to evenly distribute the leavening agents and spice throughout the dry ingredients. This ensures even texture and flavor in every cookie.
Cut the butter into smaller pieces and place it in a large mixing bowl with the brown sugar. Using an electric mixer on medium speed, cream together for 2-3 minutes until the mixture is light, fluffy, and pale in color. This aerates the dough and creates a tender crumb in the final cookie. Scrape down the sides of the bowl as needed to ensure everything is evenly mixed.
Add the room temperature eggs one at a time to the creamed butter and sugar, beating well after each addition until fully incorporated. Add the dry ingredient mixture from Step 1 in two additions, mixing on low speed after each addition just until combined—do not overmix. Fold in the chopped rhubarb and coconut by hand using a spatula or wooden spoon until evenly distributed throughout the dough. I prefer to fold these in by hand to avoid overworking the dough, which can make the cookies tough.
Preheat your oven to 350°F. Drop rounded tablespoons of dough onto ungreased baking sheets, spacing them about 2 inches apart to allow for spreading. Bake for 10-12 minutes until the edges are lightly golden but the centers still look slightly underdone—the rhubarb release moisture as they bake, so don't overbake or the cookies will dry out. Remove from the oven and let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely before frosting.
While the cookies cool, place the softened cream cheese in a clean bowl and beat with an electric mixer on medium speed for 1 minute until smooth and creamy. Add the sifted powdered sugar from Step 1 in two additions, beating well after each addition to avoid lumps. Pour in the vanilla and add the lemon zest from Step 1, beating until the frosting is light and fluffy, about 2-3 minutes total. For a tangier frosting, I like to use a bit more lemon zest—adjust to your preference.
Once the cookies from Step 4 are completely cooled, spread or pipe a generous amount of the cream cheese frosting from Step 5 onto each cookie. Work quickly so the frosting doesn't melt if your kitchen is warm. For best presentation, I like to pipe the frosting using a small offset spatula for a more polished look, but spreading with a knife works just as well.