Heat half of the olive oil in a large saucepan over medium heat.
Add the anchovy paste, finely chopped garlic, and chopped chili to the pan and sauté 1–2 minutes until fragrant.
Add the drained, lightly mashed tuna and sauté for about 10 minutes, stirring occasionally.
Stir in the canned tomatoes, then simmer the sauce over medium-low heat for 30 minutes.
About halfway through the sauce cooking, add the rinsed capers and halved pitted olives and continue cooking until the sauce is done.
While the sauce simmers (around the halfway point), bring a large pot of water to a boil. Add 2 tablespoons of coarse sea salt.
Add the angel hair pasta to the boiling water and cook about 3 minutes until al dente, then drain well.
Toss the cooked pasta with the sauce, drizzle with the remaining olive oil, and sprinkle with finely chopped parsley.
Adjust seasoning with the 1/4 teaspoon fine salt and 1/8 teaspoon ground pepper as needed, then serve immediately.
