2 oz. extra-sharp Cheddar, coarsely grated (about 1/2 cup)
2 tbsp. unsalted butter
Kosher salt and freshly ground black pepper
2 tbsp. olive oil, divided
1 small onion, sliced
1 small red pepper, sliced
2 cloves garlic, sliced
1 lb. shrimp, peeled and deveined
Pinch cayenne pepper
2 c. chicken broth
1/2 to 1 cup whole milk
Fresh cilantro leaves and lime wedges, for serving
Preheat broiler. Place poblano peppers, cut sides down, on a rimmed baking sheet. Broil, until charred, 2 to 4 minutes. Transfer to a bowl, cover, and let cool. Discard skins; dice peppers.
Bring 4 cups water to a boil in a large pot. Slowly whisk in grits. Reduce heat and simmer, stirring often (grits will bubble in spots), until liquid has absorbed and grits are tender, 20 to 25 minutes. Remove from heat and stir in cheese and butter. Season with salt.
Heat 1 tablespoon oil in a large skillet over medium heat. Add onion and red pepper. Cook, stirring occasionally, until just tender, 6 to 8 minutes. Add garlic and cook, stirring occasionally, 1 minute. Transfer to a bowl; reserve skillet.
Season shrimp with coriander, cayenne pepper, salt, and black pepper. Heat remaining tablespoon oil in reserved skillet over medium heat. Add shrimp and cook until opaque throughout, 2 to 3 minutes per side; transfer to bowl with vegetables. Add broth to skillet, increase heat to medium-high, and cook until liquid is reduced to 1 cup, 8 to 9 minutes. Return shrimp, vegetables, and poblanos to skillet and toss to combine.
Return grits to medium heat. Add 1/2 cup milk. Cook, stirring often, until heated through, 3 to 4 minutes (add additional milk as needed to thin). Serve grits topped with shrimp mixture with cilantro and lime wedges alongside.