Heat oven to 375 degrees. Pour nuts onto a small rimmed baking sheet and toast until they darken slightly and smell buttery, about 10 minutes. Set aside to cool.
Meanwhile, set chile in a small bowl and add enough boiling water to cover. When cool, drain pepper. Remove and discard seeds and stem.
Drop bread, garlic, chile and almonds into a food processor or blender. Process for a minute or so, until a thick paste forms, scraping the sides. Add the tomatoes, vinegar, paprika and olive oil and pulse.
The sauce should be of a hummus-like consistency, thick but not gluey. Add a tablespoon or two of water if it seems too dry. Add sea salt to taste.