Wash 5 limes with hot water and dry thoroughly. Zest 3 limes into a small bowl. Peel 1 lime thinly and cut the peel into fine strips; set aside for garnish.
Place 6 gelatin sheets in a bowl of cold water and soak for 5 minutes until softened. In a heatproof bowl, combine the lime zest, 4 eggs, 300 g brown sugar, and 100 ml cachaça. Set the bowl over a pot of gently simmering water on medium heat and whisk constantly for 5-8 minutes until thick and frothy and the mixture reaches 63°C (145°F) for food safety. Squeeze the soaked gelatin to remove excess water and dissolve it in the hot custard.
Squeeze juice from 4 limes into the custard. Stir in 500 g yogurt. In a separate bowl, whip 400 g cream to stiff peaks, then fold gently into the yogurt mixture.
Pour the cream into glasses (about 200 ml per glass) and refrigerate for 3 hours. Slice 1 lime and place a slice on the edge of each glass. Garnish with brown sugar and the reserved lime zest strips.