Fill a large Dutch oven with water, bring it to a boil over high heat and then season generously with salt. Cook the pasta according to package instructions, stirring occasionally, until al dente. Reserve 1 cup pasta water, strain the pasta and set both aside.
Return the Dutch oven to the stove, add 5 tablespoons of olive oil and heat over medium. Add the leeks and season with salt and black pepper. Cook, stirring occasionally, until the leeks are softened and starting to brown, 8 to 10 minutes.
Add the red pepper flakes and garlic, and stir to incorporate.
Stir in the white wine, scraping the bottom of the pan to deglaze it, and cook for 1 minute.
Add the broccolini and cook, stirring occasionally, until bright green and fork tender, 6 to 8 minutes. Transfer the vegetables to a large bowl. Wipe out the Dutch oven.
Add the butter to the Dutch oven. Once melted and foaming, sprinkle in the flour and cook, while whisking, for 1 minute. Slowly pour in the heavy cream and reserved pasta water, while whisking, until combined. Bring to a simmer, cook for 30 seconds, then remove the pot from the heat.
Sprinkle in ¾ of the cheese, a few tablespoons at a time, whisking and letting the cheese melt between each addition. Season with salt and pepper to taste.
Add the vegetable mixture, pasta and ⅔ of the chopped chives to the Dutch oven, and stir to coat in the cheese sauce.
Heat the oven to broil. In a medium bowl, toss together the bread crumbs and remaining 3 tablespoons of olive oil until well coated. Season with salt and black pepper.
Scatter half the bread crumbs over the pasta, sprinkle the remaining cheese on top and finish with the remaining bread crumbs.
Broil the pasta until the cheese is melted and the bread crumbs are deep golden brown, about 1 to 2 minutes. Garnish the pasta with the remaining chives and red pepper flakes, to taste. Serve hot.
Recipe adapted from: Epicurious