01 - On a clean work surface, mound the flour and create a well in the center. Add the eggs, olive oil, and salt into the well. Gradually draw in flour from the edges using a fork, then knead by hand for 8 to 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 to 8 minutes until softened but not browned. Remove from heat and allow to cool completely. Gently fold the cooled leeks together with the drained burrata, lemon zest, salt, and pepper until evenly combined. Take care not to overwork the burrata.
03 - Divide the rested dough in half. Working with one portion at a time, roll out on a floured surface or pass through a pasta machine 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 little water if needed. Arrange on a floured tray and repeat with the remaining dough and filling.
04 - Melt 2 tablespoons of butter in a skillet over medium heat. Add the sourdough breadcrumbs and toast, stirring frequently, for 3 to 4 minutes until golden 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 the triangoli in and cook for 3 to 4 minutes until they float and the pasta is tender yet firm. Meanwhile, melt ¼ cup of butter in a large skillet over medium heat and add the lemon juice, lemon zest, and cracked pepper. Transfer the cooked triangoli directly into the lemon butter sauce using a slotted spoon and toss gently to coat. Plate the triangoli and finish with a generous sprinkle of the toasted lemon breadcrumbs. Garnish with additional parsley if desired.