In a very large pot or saute pan over medium heat, add a drizzle of the oil from the artichokes. Add the chicken and half of the cajun seasoning and cook for about 4 minutes, then transfer to a plate.
Add the garlic and flour (plus a drizzle more of oil if it looks like it needs it and cook, stirring constantly, for about 30 seconds, then whisk in the chicken broth and add the evaporated milk and bring to a simmer (don’t let it rapid boil) until the pasta is almost cooked, then stir in the artichokes, chicken, mascarpone, spinach, half of the mozzarella and fontina, and remaining Cajun seasoning. If it feels dry, you can add a splash more broth or water to loosen.
Top with remaining cheeses and broil until browned and bubbly, about 3 or 4 minutes, watching carefully.
Let rest 5 minutes before serving.
