If using shrimp in the shell, peel and devein them. If using cleaned, thawed shrimp, skip this step. Either way, dry the shrimp well with paper towels and set aside.
Measure a generous 1/2 cup of mint leaves, somewhat loosely packed, and put them in a blender (or a mini food processor). Reserve the remaining mint leaves for garnish. To the blender, add the jalapeños, garlic, ginger, sugar, vinegar, and fish sauce (if using). Purée the ingredients until the mixture is smooth, scraping down the sides once or twice, about 3 minutes. Set the dressing aside (or refrigerate it overnight; bring it to room temperature before using).
Arrange the lettuce leaves, sprouts, cilantro, mango, and reserved mint leaves on a platter; set aside.
Set a wok or large skillet over high heat and add the oil. When hot, add the shrimp, season with salt and pepper, and stir-fry until they’re browned outside and opaque white inside, 3 to 5 minutes; cut one in half to check. Transfer to a warm platter.
To serve, bring the platters of shrimp and of lettuce and garnishes to the table. Fill a lettuce leaf with some shrimp and spoon on about 1 tsp. dressing. Add the garnishes, roll up the leaf, and eat.