Pre-heat the oven to 400°F.
Bring a large pot of salted water to a boil over high heat; 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 reserve.
Meanwhile, in a large skillet, over medium heat, heat the oil.
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.
Stir in the chopped artichokes.
Stir in the cream and bring to a simmer over medium-high heat.
Stir in the Parmesan until melted.
Remove from the heat; carefully stir in the cooked pasta, or transfer to a large bowl to mix together, if necessary; the liquid might appear wet and loose, but it will thicken up as it bakes; season to taste with salt and pepper.
Transfer the pasta to a 2-quart casserole dish or individual casseroles or ramekins.
Sprinkle with the mozzarella, place in pre-heated oven and bake until bubbling: 20 to 25 minutes.
Remove from oven and place under broiler until browned in spots; 1 to 2 minutes, if desired.
Let cool slightly before serving.
