Boil the pasta in a generous amount of lightly salted boiling water until just tender, about 8 to 10 minutes. While the pasta cooks, preheat the oven to 350 degrees F. Lightly butter an 9-x-13-inch baking dish and set aside.
Place the 3 Tbsp. butter in a medium pot set over medium heat. When the butter is melted, mix in the flour and cook, stirring, 2 minutes. Very slowly, while whisking, dribble and mix in 1/2 cup of the milk. Cook until the mixture becomes quite thick, and then slowly whisk in the remaining milk. Bring the white sauce to a simmer, stirring frequently so it does not scorch on the bottom. Simmer one minute to thicken. Remove the sauce from the heat. Mix in the oregano, paprika, cayenne, salt, pepper and three-quarters of the cheese.
When the pasta is cooked, drain it well. Add it, and the shrimp and artichokes to the sauce and gently mix to combine. Spoon the pasta mixture into the prepared baking dish. Top with the remaining cheddar cheese, and then the Parmesan cheese. Bake for 25 to 30 minutes, or until golden and bubbly.
Note: You can warm the milk for this recipe to just below a simmer in the microwave.