Preheat oven to 400°F. Cut 1/4-inch off the tops of 6 peppers, reserve tops, remove and discard stems, seeds, and membranes. Place peppers in even layer, cut side up, in a 13x9-inch baking dish, trimming bottoms of peppers to help peppers stand up straight; set aside. Chop the reserved pepper tops and remaining 1 bell pepper; set aside.
Heat 1 tablespoon of the oil in a medium saucepan over medium. Add shallot and chopped peppers; cook, stirring occasionally, until softened and lightly browned, about 10 minutes. Add garlic, smoked paprika, and red pepper; cook, stirring constantly, until fragrant, about 30 seconds. Add orzo; cook, stirring constantly for 1 minute. Add 2 1/2 cups of the chicken stock and 1 tablespoon of the salt; bring to a simmer over medium, stirring occasionally. Reduce heat to medium-low; simmer, stirring occasionally, until orzo is al dente, about 5 minutes. Remove from heat, stir in chicken and oregano until combined. Divide orzo mixture among peppers in baking dish (about ¾ cup per pepper); pour remaining 1/2 cup chicken stock around stuffed peppers; cover tightly with aluminum foil. Bake in preheated oven for 30 minutes.
Meanwhile, stir together panko, cheese, remaining 1 tablespoon oil, and remaining 1/4 teaspoon salt in a small bowl until combined. Remove peppers from oven, remove and discard foil. Sprinkle panko mixture evenly over orzo filling. Bake at 400°F until peppers are tender and panko is golden brown, about 10 minutes. Let cool for 5 minutes before serving. Garnish with fresh oregano leaves.
