Peel mangoes and cut from pit lengthwise into 1/4-inch slices. Measure 1 cup of the smallest pieces; cover and chill remaining large slices. In a blender or food processor, whirl the 1 cup mangoes and the coconut milk to a smooth purée; pour into a bowl.
In the top of a double boiler, combine egg yolks, granulated sugar, and brandy. Whisk over simmering water until mixture reaches 140°. Adjust heat to keep mixture between 140° and 150°, and continue to whisk for 3 minutes. Remove from heat and add the mascarpone cheese; stir until mixture is well blended.
In a deep bowl with a mixer on high speed, whip cream and powdered sugar until cream holds distinct peaks. Add the mascarpone mixture and fold gently to blend.
Separate ladyfinger pieces. With a fork, dip half the pieces, 1 at a time, in mango purée to coat; lift out, drain briefly, and arrange flat side down in a single layer in a 9-inch square pan. Cover ladyfingers in pan with half the mascarpone mixture, spreading it level. Repeat to dip remaining ladyfinger pieces in mango purée and arrange in a single layer over mascarpone mixture in pan. Spread remaining mascarpone mixture smoothly over top layer of ladyfingers. Cover tiramisu airtight and chill at least 2 hours or up to 1 day.
In an 8- to 10-inch frying pan over medium-high heat, stir coconut until golden, 4 to 6 minutes; pour into a small bowl. When cool, cover airtight.
To serve, cut tiramisu into 9 equal squares. Use a wide spatula to lift out portions and set on plates. Arrange reserved mango slices equally on portions and sprinkle equally with toasted coconut; spoon raspberry sauce equally around desserts.