Preheat a grill to medium high. Toss the beans, roasted red peppers, scallion, vinegar, 1/4 teaspoon salt and a few grinds of pepper in a large bowl; set aside. Toss the shrimp with 1 tablespoon olive oil, 1/2 teaspoon salt and a few grinds of pepper in another large bowl. Drizzle the cut sides of the escarole with 1 tablespoon olive oil; season with salt and pepper.
Arrange the escarole, chorizo and shrimp on the grill. Grill the escarole, turning once, until charred in spots, 2 to 4 minutes; divide among plates. Grill the shrimp and chorizo, turning once, until cooked through, about 5 minutes for the shrimp and 10 minutes for the chorizo. Add the shrimp to the bean mixture. Transfer the chorizo to a cutting board and slice into 1-inch pieces; add to the bean mixture and toss.
Spoon over the escarole; drizzle each serving with 1 tablespoon olive oil. Sprinkle with paprika.