For the chimichurri: Stir together the parsley, oil, vinegar, oregano, red pepper flakes, shallots, garlic and 1/2 teaspoon salt in a bowl. Transfer to a serving bowl and set aside.
For the shrimp and peppers: Preheat the broiler on high. Toss the shrimp with the coriander, red pepper flakes, 1/2 teaspoon salt and 1 tablespoon of the oil. Toss the peppers with the remaining tablespoon oil and 1/4 teaspoon salt.
Arrange the shrimp in a single layer on half of a large rimmed baking sheet. Arrange the peppers on the other half. Broil, flipping the shrimp and giving the peppers a stir once, until the shrimp are just cooked through and the peppers are tender and charred in spots, 6 to 7 minutes for the shrimp (remove them to a serving plate when done) and 8 to 10 minutes for the peppers. Add the peppers to the serving plate and serve with the chimichurri.