1. In a medium pot, cover eggs with cold water by 1 inch. Bring to a boil over high, cover, and immediately remove from heat. Let sit 11 minutes. Transfer eggs to a colander and run under cold water until cool enough to handle.

2. Meanwhile, in a food processor, combine red peppers, mayonnaise, mustard, and hot sauce and process until smooth, about 1 minute. Peel eggs and halve lengthwise; remove yolks, leaving whites intact. Add yolks to food processor with red-pepper mixture and process until mixture is smooth, scraping down side as needed. Season to taste with pepper. Pipe or spoon yolk mixture into whites. Sprinkle with poppy seeds before serving.