How to Make It
Preheat oven to 500°F. Place yuca in a medium saucepan, and add water to cover. Bring to a boil over high; reduce heat to medium-high, and boil until centers are translucent when cut into, about 50 minutes. Drain yuca, and spread in an even layer on a plate; let stand at room temperature until cool, 8 to 10 minutes.
Meanwhile, toss together shrimp shells, olive oil, and 1 teaspoon salt on a large rimmed baking sheet; spread in an even layer. Roast in preheated oven until shells turn red and begin to caramelize, about 30 minutes, stirring every 10 minutes.
Roast bell peppers over a gas flame or under a broiler heated to high, turning with tongs until skins are blackened all over, 10 to 12 minutes. Place in a bowl, and cover with plastic wrap. Let stand at room temperature until cool enough to handle, about 15 minutes.
Meanwhile, smash garlic on a cutting board; sprinkle with 1 teaspoon salt. Using flat side of a large knife, drag knife back and forth over garlic to form a paste.
Peel charred skin off bell peppers; discard skin and seeds. Coarsely chop peppers. Combine peppers and garlic paste in blender, and process until smooth, about 40 seconds, stopping to scrape down sides as needed. Set bell pepper paste aside.
Add white wine to baking sheet with shrimp shells. Using a metal spatula, scrape up shells and browned bits.
Chop cilantro stems and leaves to equal 1 cup; chop scallions to equal 1/2 cup. Combine chopped cilantro, chopped scallions, shrimp shells, onion, and carrot in a medium stockpot. Add 16 cups water, and bring to a boil over high. Reduce heat to low, and simmer until broth has a shrimpy aroma, about 40 minutes. Pour mixture through a fine wire-mesh strainer into a large stockpot; discard solids. Set broth aside.
Press yuca, in batches, through a ricer into a medium bowl. Chop cilantro leaves to equal 3 tablespoons, and thinly slice scallions to equal 1/3 cup. Combine chopped cilantro leaves, sliced scallions, yuca, raw shrimp, egg, lime zest, 2 tablespoons bell pepper paste, and 11/2 teaspoons salt in a bowl. Turn mixture out onto a work surface, and knead until combined. Shape into 36 (1/2-ounce) balls; arrange balls on a baking sheet. Refrigerate until thoroughly chilled and set, about 30 minutes.
Bring shrimp broth to a simmer over medium-high. Whisk in butter, 3/4 cup bell pepper paste (reserve remaining paste for another use), and remaining 1 teaspoon salt. Stir in collard greens. Add dumplings, and cook, maintaining a simmer, until dumplings are cooked through, about 4 minutes.
Thinly slice 1 scallion, and chop remaining cilantro. Ladle soup into bowls. Garnish each bowl with 1 teaspoon thinly sliced scallion, 1 teaspoon chopped cilantro, and a drizzle of chile oil. Serve with lime wedges.