Heat 3 tablespoons of the olive oil in a heavy pot over medium-high heat.
Add the tomato paste and cook, stirring for 5 minutes.
Add the paprika, thyme, and oregano and cook until toasted and aromatic, about 1 minute.
Add the canned tomatoes, water, sausage, and fennel and bring to a simmer and cook until fennel is tender, about 15 minutes. (if making ahead of time, remove from the heat and refrigerate until ready to finish. Reheat gently before proceeding).
Add the clams and increase the heat to high.
Simmer vigorously until the clams open, 7 to 10 minutes.
Discard any clams that don't open.
Stir in the Madeira and vinegar.
Divide among 4 bowls and drizzle remaining 2 tablespoons of olive oil over the top. Serve at once!