In a large pot over high heat, bring eggs, vinegar, and enough cold water to cover by 1 inch to a boil. Reduce heat to medium-high to maintain a medium boil and cook eggs for 8 minutes. Drain and run eggs under cool water. Fill a bowl with cold water, add eggs, and let sit for 20 minutes to cool at room temperature.

Peel eggs and halve horizontally. Cut off the tips so that the eggs will stand upright. Remove yolks and transfer to a medium bowl. Set aside white egg cups on a serving plate.

Place the yolks in the bowl of a food processor and process just long enough to break up yolks.

To yolks, add Cheddar cheese, cream cheese, mayonnaise, diced roasted red pepper, dry mustard, salt, and freshly ground pepper. Process until light and fluffy. Place the mixture in a pastry bag fitted with a star tip and pipe the mixture into the egg white cups. Cover and refrigerate for at least 30 minutes, or until ready to serve.