1/4cup plus 2 tablespoonsfinely grated (ground) Parmesan cheese
Bring a large pot of salted water to a boil. Add the pasta and cook until 2 minutes short of al dente. Drain and set aside.
Meanwhile, preheat the oven to 400 degrees F. Lightly coat a 2-quart or 9-inch round baking dish with nonstick spray. In a large deep skillet or Dutch oven, cook the bacon over low heat until it is crisp and the fat is rendered, about 10 to 15 minutes. Stir periodically and don’t rush the process. With a slotted spoon, remove the cooked bacon from the skillet and transfer to a paper-towel-lined plate. Set aside. Drain all but 2 tablespoons fat from the skillet (you may not need to drain the pan at all). Increase the heat to medium high.
While the bacon cooks, trim off the ends of the brussels sprouts and cut them into very thin slices or shave them on a mandoline. Add them to the pot with the reserved bacon fat and sprinkle with salt and pepper. Cook, stirring often, until brighter green in color but barely wilted, 2 to 3 minutes. Add the garlic and lemon zest and cook 1 minute. Sprinkle the flour over the top and stir until blended, about 1 minute more.
Splash in the broth about 1/4 cup at a time, stirring constantly to blend between additions and prevent lumps from forming. Let simmer until slightly thickened, 2 to 3 minutes. Remove from the heat and stir in the lemon juice, then the cooked pasta; stir to coat evenly. Stir in the Greek yogurt, 1/3 cup cheddar cheese, 1/3 cup mozzarella cheese, and 1/4 cup Parmesan cheese.
Scrape the pasta mixture into the prepared baking dish and sprinkle with the remaining 1/3 cup cheddar and 1/3 cup mozzarella, then the cooked bacon, then the remaining 2 tablespoons Parmesan. Bake until bubbly around the edges and browned in spots on top, 25 to 30 minutes. Serve hot.