Preheat the oven to 450 degrees F. Line a baking sheet with aluminum foil. Toss the chicken, 1 tablespoon olive oil, the paprika, 1/2 teaspoon salt and 1/4 teaspoon pepper in a bowl; spread in a single layer on the baking sheet. Roast until just cooked through, 15 minutes. Transfer the chicken to a cutting board; discard the foil and reserve the baking sheet. Heat 1 tablespoon olive oil in a skillet over medium-high heat; add the onion and cook, stirring occasionally, until golden, 6 to 8 minutes. Add the garlic, 1/4 teaspoon salt, and pepper to taste and cook, 1 minute. Remove from the heat and stir in the pickled peppers. Brush the insides of the rolls with the remaining 1 tablespoon olive oil; arrange cut-side up on the baking sheet and toast in the oven, about 2 minutes. Thinly slice the chicken and divide among the rolls. Top evenly with the onion mixture and the cheese. Return to the oven to melt the cheese, about 2 minutes. Top with hot sauce and/or ketchup and serve with carrot and celery sticks.