Set a cast iron skillet on a grill, cover it, and preheat it to high. In a small bowl, combine the shallots, salt, sugar, chile, lime juice, and herbs. Drizzle in the olive oil, stirring to combine. Taste. Adjust with more salt, sugar, vinegar (for more bite) or oil (for less bite). If you would like it hotter, add a pinch of crushed red pepper flakes.
Place the shrimp in a large bowl and season generously with kosher salt.
When the grill temperature has climbed to 550° F or so, pour the tablespoon of neutral oil into the skillet. Carefully add the shrimp. Shake the skillet to distribute the shrimp, cover the grill, and cook for 2 minutes. Uncover, shake again, and cook for 30 seconds to 1 minute more.
Transfer shrimp to a large bowl. Toss with about half of the chimichurri. Transfer shrimp to a platter and serve immediately, with more chimichurri on the side.