01 - On a clean work surface, mound the flour 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 until a shaggy dough forms. Knead firmly by hand for 8 to 10 minutes until the dough is smooth, supple, and springs back when pressed. Wrap tightly in plastic and rest at room temperature for 30 minutes.
02 - Melt 2 tablespoons of butter in a sauté pan over medium heat. Add the chopped leeks and cook gently for 6 to 8 minutes, stirring occasionally, until completely softened but without any color. Transfer to a plate and cool to room temperature. In a mixing bowl, combine the cooled leeks with drained burrata, lemon zest, salt, and pepper. Fold gently until evenly distributed.
03 - Divide the rested dough in half and keep one portion wrapped. Roll out the first portion 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 diagonally 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 dry skillet over medium heat, melt 2 tablespoons of butter. Add the sourdough breadcrumbs and stir continuously for 3 to 4 minutes until deeply golden and crisp. Remove from heat, stir in the lemon zest, chopped parsley, and a pinch of salt. Transfer to a bowl and set aside.
05 - Bring a large pot of well-salted water to a gentle boil. Drop in the triangoli and cook for 3 to 4 minutes until they float and the pasta is tender but still has a slight bite. 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 immediately, showering generously with the toasted breadcrumbs and an extra sprinkle of parsley if desired.