Preheat broiler on low and line a baking sheet with aluminum foil.
Halve the peppers and tomato, then place both, along with the whole garlic cloves, on the baking sheet (skin side up).
Broil the vegetables for 10 to 12 minutes, or until the skin becomes charred.
Remove the vegetables from the broiler, then place them on a plate. Cover the plate with aluminum foil for 15 minutes.
Remove the foil. Peel the peppers and tomato and remove the seeds from the tomato. Place to the side.
Toast the almonds.
While the vegetables are covered for 15 minutes, place the slivered almonds on an aluminum foil-lined baking sheet.
Place the baking sheet in a toaster (or in the oven at 350 degrees Fahrenheit). Toast the almonds for 2 to 4 minutes (until lightly browned), then remove from the toaster. Set to the side.
Make the sauce
In a large bowl, combine the peeled peppers, tomato, and garlic. Pulse blend using a food processor until you reach a rough chop.
Add the almonds and bread and pulse blend the sauce again until combined.
Add the olive oil, sherry vinegar, smoked paprika, and cayenne pepper. Pulse blend the sauce until smooth (or your desired consistency).
Add the salt, to taste.
Serve immediately or store covered in the refrigerator for up to one week.