Preheat oven to 425F
Bring a large pot of water to a boil, then add a generous amount of salt. Cook pasta, stirring occasionally to keep it from sticking together, until just barely al dente, about 2 minutes less than package directions. Drain pasta, reserving 1 cup pasta cooking liquid
While you are cooking the pasta heat 5 tbsp oil in a large Dutch oven or other heavy pot over medium–high. Add leeks and season with salt and black pepper. Cook, stirring occasionally, until leeks are softened (but not so much that they don’t have any texture left) and starting to brown, 8–10 minutes
Add red pepper flakes to leeks and stir to incorporate. Add broccolini by the handful, stirring to combine and allowing each addition to wilt before adding more. Season with salt and black pepper. Once all of the broccolini has been added, cook, stirring occasionally, until bright green and wilted, about 2 minutes. Remove pot from heat and set aside
Add pasta to reserved broccolini mixture along with cream, three-quarters of the cheese, 1/2 cup chives, and reserved pasta cooking liquid; mix well. Season with salt and black pepper and add more red pepper flakes if you prefer more heat. Keep in mind that the saltiness and spiciness will increase slightly as the pasta bakes
Transfer pasta to a 3-qt. baking dish. Toss breadcrumbs and remaining 3 tbsp oil in a medium bowl until coated; season with salt and black pepper. Scatter over pasta, then sprinkle evenly with remaining cheese. Bake until pasta is bubbling across the entire surface and breadcrumbs are deep golden brown, 30–35 minutes. Let cool slightly
Scatter remaining chives over pasta before serving