01 - Mound the flour on a clean work surface and create a deep well in the center. Add the eggs, olive oil, and salt into the well. Using a fork, gradually draw in flour from the inner walls of the well until a shaggy dough forms. Knead by hand for 8–10 minutes until the dough is smooth, elastic, and springs back when pressed. Wrap tightly in plastic wrap and rest at room temperature for 30 minutes.
02 - Melt 2 tablespoons of butter in a skillet over medium heat. Add the chopped leeks and sauté for 6–8 minutes until softened and translucent, taking care not to let them brown. Allow the leeks to cool completely, then gently fold together with the drained burrata, lemon zest, salt, and pepper until evenly combined. Set aside.
03 - Divide the rested dough in half and keep one portion wrapped. Roll out the dough on a lightly floured surface or pass it through a pasta machine, working down to approximately 1 mm thickness. Cut the sheet into squares about 3 inches per side. Place 1 teaspoon of filling in the center of each square, fold into a triangle, and press the edges firmly to seal, dabbing with a touch of water if needed. Arrange on a floured tray and repeat with the remaining dough and filling.
04 - In a skillet over medium heat, melt 2 tablespoons of butter. Add the sourdough breadcrumbs and toast, stirring frequently, for 3–4 minutes until golden brown and crispy. Remove from heat and stir in the lemon zest, chopped parsley, and a pinch of salt. Set aside.
05 - Bring a large pot of generously salted water to a gentle boil. Drop in the triangoli and cook for 3–4 minutes until they float and the pasta is tender yet firm. Meanwhile, melt 2 oz of butter in a large skillet over medium heat. Add the lemon juice, lemon zest, and several cracks of black pepper. Using a slotted spoon, transfer the cooked triangoli directly into the lemon butter sauce and toss gently to coat. Plate the triangoli, sprinkle generously with the toasted breadcrumbs, and garnish with additional parsley if desired.