In bowl, beat flour, cocoa powder, nutmeg, butter, sugar and salt on medium-high speed just until butter is incorporated. Add egg; beat just until dough forms; do not overmix. Pat into thick disk; wrap; refrigerate 2 hours (or up to 5 days, or freeze for up to 4 weeks). Dough will darken.
Heat oven to 310°F. In small bowl, sprinkle gelatin over the 1/4 cup cold water. Let stand until gelatin has absorbed all the water, about 1 minute.
In 2-quart heavy-bottomed saucepan, combine coconut milk, sugar, rum and lime zest. Place over medium-high heat. Split vanilla bean in half lengthwise; scrape seeds into milk; add bean. Add gelatin. Heat, stirring occasionally, until bubbles begin to appear around edge of saucepan; do not boil. Remove from heat. Remove vanilla bean.
Pour hot liquid into tall container or large measuring cup. Mix with hand-held immersion blender about 30 seconds or just until thickened emulsion forms. Or whisk very well. Slowly add egg whites while continuing to blend. Blend until smooth, about 45 seconds.
Coat twelve 4 x 1-inch individual tartlet pans with nonstick cooking spray. (Or coat two 13 x 9 x 2-inch baking pans.) Pour 1/3 cup coconut mixture into each tart pan. (Or divide coconut mixture between 2 pans.) Place tart pans on rimmed baking sheet with 1-inch high sides. Place baking sheet in 310°F oven. Add enough hot water from tap to baking sheet to come halfway up sides of tart pans. (Or place 2 pans in water baths.)
Bake tart pans in 310°F oven 40 minutes, until custard trembles slightly when tarts are gently shaken. (Or 2 pans in water baths 25 minutes.) If any liquid is under skin, custard is underbaked. Return to oven; shake every 5 minutes until ready. Transfer pans to wire rack; let cool 30 minutes. Refrigerate 2 hours before serving, or overnight.
Heat oven to 400°F. Line baking sheet with parchment paper. Divide dough in half. Place half on floured work surface; return other half to refrigerator. Using rolling pin, lightly hit dough with few quick raps to soften. Roll into 1/4-inch-thick rectangle. Use 3-1/2-inch round fluted cutter to cut 12 circles (re-roll scraps). Place circles, 2 inches apart, on prepared baking sheet. Repeat with rest of dough. Sprinkle with grated coconut, if desired.
Bake in 400°F oven until firm to touch, 10 to 12 minutes. Transfer cookies to wire rack; let cool. (Cookies can be stored at room temperature, wrapped in plastic wrap, for up to 1 week, or in the freezer for up to 4 weeks.)
Place 1 cookie in center of a plate. Run paring knife around edge of tartlet pan; invert filling onto cookie. (If it doesnt unmold easily, dip bottom of pan in hot water.) Cover with another cookie. (Or use 3-1/2-inch cutter to cut out 6 circles from each baking pan of filling. With cooking spray-coated spatula, slide circles onto cookies.) Serve immediately. Repeat with the remaining filling and cookies for the number of desired servings.