Place the mango, lime and sugar for the sauce in a blender or food processor and blend until smooth.
Transfer the puree to a small saucepan and warm over a medium heat to bring it to a simmer. Cook, stirring regularly, for around 10 minutes until it has thickened slightly (will likely reduce by around ¼ to ⅓ and be slower to re-join behind a spatula drawn through the mixture). Remove from the heat and allow to cool to room temperature. Alternatively, make ahead and chill.
To make panna cotta
Put the milk in a small bowl and add the gelatin. You can either just leave it or gently stir first (check method suggested on packet) then leave approx 5min to bloom (as you prepare cream). The gelatin will absorb liquid and become more of a wobbly solid.
Measure out ⅓ cup (80ml) of the mango puree ready to use. Gently warm the cream and sugar in a small pan over a medium-low heat. You just want to warm the mixture enough to dissolve the sugar, but don't let the mixture boil.
Remove the cream from the heat and add the milk-gelatin mixture and the ⅓ cup of mango puree and mix all well.
Divide the mixture between two ramekins/custard dishes or glasses and chill for at least 2 hours.
Once the panna cotta has set, spoon over the remaining mango sauce on top of the panna cotta and spread to forma thin layer. If you like, top with eg a little whipped cream and some small chunks of mango.
Fresh mango generally has the best flavor and so is what I would recommend for this. Try to choose a variety that is nicely sweet and without tough fibers. You can also use frozen, defrosted mango.