Heat the oven to 400℉. Bring a large pot of salted water to a boil over high. Turn down to medium-high, and cook the pasta according to package instructions until 2 minutes short of al dente (the pasta will finish cooking in the oven). Drain and set aside.
Meanwhile, heat the oil in a large skillet over medium. Add the garlic and red-pepper flakes and cook until fragrant, about 1 minute. Add the spinach little by little until wilted, stirring frequently, about 3 minutes. Transfer to a bowl and set aside.
Wipe the skillet and add butter until melted. Add the flour and stir for a few seconds. Add the milk and stir vigorously until the flour and milk are blended. Turn up the heat and gently bring it up to a boil. Add the salt, nutmeg, oregano and black pepper. Cook for 2 minutes, until it begins to thicken.
Remove from the heat then carefully stir in the cooked spinach, artichokes, 1/2 of the mozzarella, parmesan and cooked pasta. The cheese sauce might appear liquidy and thin, but it will thicken up as it bakes. Season to taste with salt and pepper if needed.
Transfer the pasta to a baking dish. Sprinkle with the remaining mozzarella and parm, bake until bubbling, 20 to 25 minutes. Broil until browned in spots, 1 to 2 minutes, if desired. Let cool slightly before serving.