Whisk eggs and sugar together in large saucepan until mixture thickens. Add butter slowly, whisking to blend. Gently mix in coconut and vanilla extract with wooden spoon. Sprinkle flour evenly over mixture and blend well.
Place pan over medium heat and cook, stirring constantly, until mixture is thick and dry, about 10 minutes. (The only issue I had was the recipe says to cook until dry, it doesn't get dry, just thick and more like batter.) Transfer mixture to large bowl, cover and refrigerate until cool; 3 to 4 hours.
Preheat oven to 350°F. Shape about 2 tablespoons of dough into small “mountain” shapes and place on parchment-lined cookie sheets. Bake 18 to 22 minutes, rotating pans halfway through baking, until lightly browned. Cool completely on a wire rack.
Melt bittersweet chocolate in small saucepan over low heat, stirring constantly (I make it a double boiler, water in pan and bowl with chocolate on top). Dip pointy ends of macaroons in chocolate, leaving small area around the bottom exposed. Place cookies on wax paper and let stand until chocolate is firm. Melt white chocolate over low heat in clean saucepan, stirring constantly. Dip top points of each cookie into white chocolate to add “snow cap.” Allow white chocolate to set at least 3 hours.
Store in airtight container in refrigerator for up to 3 days.