Cook the Pasta: Bring a large pot of salted water to a boil. Prepare the pasta following the package instructions, cooking it until it reaches an al dente texture. Drain and set aside.
Cook the Bacon and Brussels Sprouts: In a large skillet over medium heat, cook the bacon lardons until crisp. Using a slotted spoon, transfer the bacon to a paper towel-lined plate to drain. Leave about 1 tablespoon of the bacon fat in the skillet for later use.
Sauté the Brussels Sprouts: In the same skillet, add the Brussels sprouts and season with ½ teaspoon salt and ½ teaspoon black pepper. Sauté over medium heat until they are tender and slightly caramelized, about 8-10 minutes. Add the minced garlic and lemon zest, cooking for another minute until fragrant. Remove from heat.
Prepare the Cheese Sauce: In a medium saucepan, whisk together the flour and remaining ½ teaspoon salt and ½ teaspoon black pepper over medium heat. Slowly add the broth, whisking constantly to prevent lumps, and cook until thickened, about 3-4 minutes.
Add Greek Yogurt and Cheese: Remove the saucepan from heat and stir in the Greek yogurt, ⅓ cup cheddar cheese, ⅓ cup mozzarella cheese, and all but 2 tablespoons of the Parmesan cheese. Mix continuously until the cheese is fully melted and the sauce becomes smooth and creamy. Add the lemon juice to the sauce and mix well.
Combine Everything: Add the cooked pasta, bacon, Brussels sprouts, and cheese sauce back to the large skillet. Stir to combine everything thoroughly. Top with the remaining cheddar, mozzarella, and saved Parmesan, scattering them evenly over the dish.
Bake: Preheat your oven broiler. Transfer the skillet to the broiler for 2-3 minutes, or until the cheese is melted, bubbly, and golden brown on top. (Watch closely to avoid burning.)
Serve: Remove from the oven and let cool slightly. Serve warm, garnished with additional lemon zest or parsley if desired.