How to Make It
Make the garlic-herb oil: Set a large heatproof bowl in an ice bath.
Pour 3 cups grapeseed oil into a large saucepan. Cook over moderate heat until shimmering.
Add parsley, cilantro, basil, mint, and garlic to the oil. Fry, stirring, until the herbs are bright green and fragrant, about 15 seconds.
Working carefully and quickly, pour oil mixture into a blender. Begin blending on low, gradually increasing speed to high until the herbs are completely incorporated, about 2 minutes.
Pour the garlic-herb oil into the prepared bowl, and fold until the mixture is chilled, about 1 minute. Add 2 teaspoons lime zest, Champagne vinegar, kosher salt, and cayenne, and stir to combine. Chill garlic-herb oil until ready to serve.
Make the shishito peppers: Heat a 12-inch cast-iron skillet over high heat. Toss the peppers with 2 tablespoons oil and kosher salt. Add half of the peppers to the pan. Cover and cook the peppers until charred, about 8 minutes.
Uncover the peppers and toss until just cooked through, about 10 seconds. Place cooked peppers in a bowl. Repeat procedure with the remaining peppers. Dress warm peppers with 1 tablespoon lime juice and flaked salt.
To serve, season the garlic-herb oil with 1 teaspoon lime juice and transfer to a large shallow bowl set on a large serving platter. Arrange the shishito peppers around the bowl for dipping, and sprinkle the peppers with 1 teaspoon lime zest.