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 until a shaggy dough forms. Knead by hand for 8 to 10 minutes until the dough is smooth, supple, 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 to 8 minutes until softened and translucent, taking care not to brown them. 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 to approximately 1 mm thickness. Cut 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 toast, stirring frequently, for 3 to 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 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 and stir in the lemon juice, lemon zest, and a few generous 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, spooning any remaining sauce over the top, and finish with a generous scattering of the lemon butter breadcrumbs. Garnish with additional parsley if desired.