1 (1/4-ounce) New Mexico chile, stemmed

1 cup (8 ounces) unsalted butter, softened

¼ cup packed fresh cilantro leaves and tender stems, chopped

1 teaspoon cumin seeds, toasted and ground

16 jumbo (U-10 ) unpeeled raw Gulf shrimp, head-on, tail-on (about 1 1/2 pounds)

2 teaspoons, plus 2 tablespoons canola oil, divided

¾ cup sliced (1/2-inch pieces) okra

⅓ cup chopped yellow onion (from 1 small [6 ounce] onion)

33 cup chopped seeded poblano chile (from 1 small [2 ounce] chile)

1 tablespoon minced garlic (from 3 garlic cloves)

1 cup (5 ounces) cherry tomatoes, halved

¾ cup fresh corn kernels (from 2 [7 ounces total] ears)

¾ cup chopped summer squash (from 1 small [5-ounce] squash)

¾ cup yellow hominy (from 1 [15 1/2-ounce] can), drained

Bring water to a boil in a medium saucepan over high. Remove from heat; add chiles. Cover and let soak until softened, about 15 minutes.

Transfer chiles and 1/3 cup of the soaking water to a tall jug. Using an immersion blender, process until smooth, about 2 minutes.

Place softened butter in a large bowl. Stir in blended chile mixture, cilantro, cumin, and salt using a flexible spatula until well combined.

Transfer butter mixture to an airtight container. Store in refrigerator up to 3 days.

Peel and devein shrimp, leaving tails on; reserve shells. Place shrimp on a plate, and refrigerate until ready to use. Heat 2 teaspoons of the oil in a medium saucepan over medium-high. Add shrimp shells; cook, stirring often, until fragrant, about 2 minutes. Add water, and bring to a boil over medium-high. Reduce heat to medium-low; simmer, undisturbed, 20 minutes. Remove from heat. Pour through a fine mesh strainer into a heatproof bowl; discard solids. Measure 3/4 cup strained liquid into a small bowl, and set aside. Reserve remaining shrimp stock for another use.

Heat a small skillet over medium-high. Add cumin seeds; cook, swirling or stirring often, until fragrant and dark brown, 1 to 2 minutes. Transfer toasted seeds to a spice grinder; process until a fine powder forms, about 30 seconds. Transfer to a small bowl, and set aside.

Heat 1 tablespoon of the oil in a cast-iron skillet over medium-high until very hot. Add lime halves, flesh-side down, and cook until limes are charred on cut side, about 3 minutes. Transfer limes to a plate and set aside. Add okra to skillet; cook, stirring occasionally, until lightly charred, 4 to 5 minutes. Remove from heat, and set aside.

Heat remaining 3 tablespoons oil in a large skillet over medium-low. Add onion, poblano, and garlic; cook, stirring often, until softened and translucent, 8 to 10 minutes. Increase heat to medium-high. Add okra, tomatoes, corn, summer squash, hominy, paprika, cumin, and salt; cook, stirring often, until vegetables are tender, 2 to 3 minutes. Remove from heat. Cover, and set aside to keep warm.

Heat remaining 2 tablespoons oil in a large skillet over medium-high. Add shrimp and 1/2 teaspoon of the salt; cook until pink but not yet fully cooked, about 1 minute per side. When shrimp are nearly done, pull off the burner; pour in mezcal and reserved shrimp stock. Return to medium-high heat, and bring to a boil. When large bubbles form in the liquid, about 1 minute, reduce heat to low; gradually stir in Chile Compound Butter to form an emulsified sauce. Stir in remaining 1/4 teaspoon salt.

Divide Summer Succotash evenly among 4 plates. Top evenly with Drunken Shrimp, sauce in skillet, and 1 charred lime half. Serve immediately.