Preheat a grill to medium-high (400°F to 450°F), or heat a grill pan over medium-high. Brush quartered bell pepper and halved jalapeño evenly with 1/2 tablespoon of the oil. Grill, uncovered,turning occasionally, until slightly charred on both sides, about 5 minutes per side. Transfer to a small bowl and cover with aluminum foil. Chill at least 30 minutes and until ready to serve.
Place remaining 1 tablespoon oil in a large skillet; heat over medium-high. Add onion; cook, stirring often, until softened, about 5 minutes. Add corn and garlic; cook, stirring often, 3 minutes. Stir in broth, salt, and black pepper. Bring to a boil over high; reduce heat to medium-low and simmer, stirring occasionally, 6 minutes.
Pour corn mixture into a blender. Remove center piece of blender lid to allow steam to escape; secure lid on blender and place a clean towel over opening to prevent splatters. Process until smooth, about 2 minutes. Pour into a medium bowl; stir in lime juice and cumin. Cover and chill until completely cold, at least 4 hours.
Chop chilled roasted bell pepper and jalapeño; stir into chilled corn mixture. Stir in cilantro. Ladle soup into 4 serving bowls. Top evenly with shrimp and chopped avocado; garnish with additional cilantro. Serve immediately.