Prepare a 9-inch square pan by lining bottom and sides with plastic wrap, having wrap hang over edges of the pan. Alternatively, you can use glasses or ramekins for this as well.
For citrus base, bring the blood orange juice, lime juice, rum, mint extract and cream to a simmer in a saucepot. Then turn the heat off.
In a bowl, whisk egg yolks with sugar and cornstarch. Slowly add some of the cream to the egg mixture, whisking constantly, and keep adding cream until it has been fully blended into the eggs. Don't add too much at once or it will cook the eggs. Return mixture to the stove and cook over medium heat, whisking constantly until thickened and glossy, only about 2 to 3 minutes. Remove from heat and strain.
Soften gelatin in cold water for 2 minutes, then whisk into hot custard. Set aside to cool at room temperature (do not chill).
For the meringue, bring sugar and water to a simmer. Simmer for 5 mins and then bring to a boil and cook on high heat until sugar registers 240 °F on a candy thermometer, about 3 minutes. Take off the heat and remove the mint.
While sugar is boiling, whip egg whites until they hold a soft peak (the peaks bend when whisk is lifted). Slowly and carefully pour in hot sugar down the side of the bowl with the meringue, whipping constantly (pouring it down the side of the bowl will prevent splashes of hot sugar), and whip the whites on medium speed until they have cooled to barely warm.
Fold a third of the meringue into the citrus base and then fold in the remaining two thirds until incorporated.
Scrape mousse into prepared pan and spread evenly. Chill until firm, about 4 hours or less if using smaller containers.
Top with segments of blood orange and a sprig of mint and serve.