Light a grill or preheat the broiler. Set the bell peppers over a hot fire or under the broiler and cook, turning, until charred all over. Transfer the bell peppers to a plate and let cool.
Peel the roasted peppers and discard the cores and seeds. Cut the peppers into 1/8-inch dice and pat dry with paper towels.
In a medium bowl, mix the diced peppers with the cheddar, cream cheese, mayonnaise, pickle juice and Tabasco and season with salt and pepper. Cover and refrigerate for at least 2 hours. Serve with crackers.