1. Make the olive crumble – can also be prepared a day in advance
Preheat the oven to 140°C. Set aside a generous tablespoon of olives in the jar for later use in the pasta sauce. Spread the remaining olives on a baking tray lined with parchment paper and let them dry in the oven for 2–3 hours. Allow them to cool completely, then grind them into a crumble.
2. Cook the sauce
Heat the olive oil in a frying pan over medium heat. Add the anchovies and stir until they are almost dissolved into the oil. Add the garlic and chili flakes and sauté briefly. Pour in the passata and add a pinch of sugar, the chopped olives, and the capers. Let the sauce simmer gently for about 10 minutes. Stir in most of the parsley, keeping a little aside for garnish.
3. Cook the pasta
Boil the spaghetti for 7 minutes until al dente. Reserve some of the pasta water, then drain. Add the spaghetti to the sauce along with 1–2 tablespoons of the reserved pasta water and mix well. Taste and adjust with black pepper and, if needed, a little salt.
4. Finish and serve
Divide the spaghetti between plates. Tear open the burrata and spoon the creamy centre over the pasta. Drizzle with extra olive oil, sprinkle with chili flakes and lemon zest, and top with the olive crumble and reserved parsley.