In a stainless steel bowl, whisk together egg whites, sugar, honey and vanilla until blended. Place over a pan of simmering water and cook, whisking occasionally, until hot, about 2 minutes. Remove bowl from heat and stir in coconut and flour until incorporated. Refrigerate dough until firm, about 1 hour.
Preheat oven to 325 degrees. Line 2 baking sheets with parchment paper.
To shape each cookie, using a small spoon or ice cream scoop, scoop up the dough into 1-inch balls. As the cookies are formed, place them on the prepared baking sheets, spacing them about 2 inches.
Bake until golden brown, about 15 minutes. At the midway point, switch the pans between the racks and rotate them 180 degrees to ensure even baking. Let cool on the pans to room temperature.
Melt chocolate in a double boiler. Whisk until smooth and let cool until warm. Line the baking sheets with fresh parchment paper. With a table knife or small icing spatula, spread a thin layer of chocolate on the bottom of each macaroon. Place the cookies, chocolate side down, on the prepared baking sheets. Let stand until chocolate is set, about 1 hour.
Planning ahead: The macaroons may be made 2 days ahead. Store in an airtight container at room temperature.
Makes 36 cookies
Classic Stars Desserts (Chronicle Books 2007)