Bring a large pot of salted water to a boil. Add the trenette or linguine and cook according to package instructions until al dente. Reserve 1 cup of pasta water, then drain the pasta.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and red pepper flakes (if using) and sauté for about 1 minute until fragrant.
Add the cooked pasta to the skillet along with the lemon zest, lemon juice, and half of the reserved pasta water. Toss to combine, adding more pasta water as needed to create a light sauce. Season with salt and pepper to taste.
In a separate pan, toast the breadcrumbs over medium heat until golden brown, about 3-4 minutes. Remove from heat and stir in the chopped parsley.
Serve the pasta in bowls, topped with stracciatella cheese and the toasted breadcrumb mixture. Finish with grated Parmesan cheese.