1. Grease and flour a 9-inch round cake pan. Preheat oven to 350 degrees. Grate rind of one grapefruit to measure 1 tablespoon zest. Squeeze same grapefruit to yield 1/2 cup unstrained juice. Cut half grapefruit into segments. Reserve all separately.
2. To prepare cake, cream butter on medium speed on mixer in a large bowl, gradually beating in sugar until fluffy. Add 2 egg yolks and whole egg; beat well. Combine flour, baking powder, and zest, and add alternately with milk and juice to the butter mixture, beginning and ending with flour mixture and beating well after each addition; stir in vanilla. Pour batter into prepared pan. Bake at 350 degrees for 28 to 30 minutes until pick inserted in center tests clean. Cool in pan 10 minutes. Remove from pan to cool completely.
3. To prepare filling, combine egg yolks and water. In a heavy saucepan, combine sugar and flour; add yolk mixture and zest. Cook over medium heat, stirring, until mixture thickens and boils. Remove from heat; stir in juice and butter. Cover loosely and cool. Place cooled cake on baking sheet. Spoon filling evenly on cake to within 1/2 inch of edges.
4. To prepare topping, beat the four egg whites (at room temperature) with cream of tartar for 1 minute on high speed. Gradually add sugar/grapefruit zest mixture, beating until stiff peaks form, about 3 minutes. Spread topping over cake filling, covering completely. Using back of tablespoon, form decorative swirls from center to edges.
5. Bake at 350 degrees for 12 to 15 minutes until peaks are lightly browned. Cool completely. Just before serving, decorate center top with reserved, well-drained grapefruit segments and, if desired, a sprig of fresh mint.