For the shrimp: Bring a large pot of salted water to a boil. Turn off heat, add shrimp, and let stand in water until just cooked through, about 3 minutes. Drain and cool. Peel shrimp, leaving tails on, and devein. Season shrimp with salt. Refrigerate until ready to serve.
For the serrano-mint sauce: Place all ingredients, except for salt, in a blender. Pulse until smooth. Season with salt. Cover and refrigerate until ready to use. Bring to room temperature before serving.
Bring shrimp to room temperature just before serving. Drizzle with chili oil, if using. Sprinkle shrimp with a few cilantro leaves. Serve shrimp with serrano-mint sauce for dipping.