For the shrimp and mango summer rolls: Fill a large bowl with water and add ice cubes. Bring a large saucepan of salted water to a boil, add the shrimp and blanch until just cooked through, 3 to 5 minutes. Drain and transfer to the bowl with ice water to stop the cooking. Let the shrimp sit in the ice bath for 2 minutes, then drain and pat dry the shrimp, slice horizontally in half and transfer to a medium bowl. Add the mangoes, lime juice, fish sauce and sambal, season with pepper and stir to combine.
Fill a dish with hot tap water. Add a wrapper for 2 seconds only and transfer the wrapper to a lint-free towel to drain, top with a second towel and blot dry. Flip over the stack of towels and peel off the top towel. Top the wrapper with 2 to 3 Thai basil leaves and the shrimp and mango filling. Fold up the bottom and force the filling downwards to form a log. Then fold in both sides then continue rolling. Store under a damp towel to keep moist. Repeat with remaining rolls. Halve each roll on the diagonal and serve immediately.
Make the lime dipping sauce: Mix all the ingredients in a bowl and serve with the rolls.