Preheat the broiler with the pan 4 inches from the heat.
Cut the flat panels off the peppers and place them skin-side up on the broiler pan. Broil until charred, about 10 minutes. Transfer to a plate, one on top of the other (no need to cover with plastic wrap) and let sit until cool enough to handle. Peel and transfer to a food processor.
Preheat the oven to 350 degrees F.
Brush the slices of bread with some oil (or if you prefer you can leave them dry) and toast until crisp, about 10 minutes.
Add the goat cheese, olive oil, paprika, pepper flakes and salt to the food processor with the peppers and process until smooth. Transfer to a bowl and serve with the crostini or crackers.