Cook the pasta al dente in well-salted water (it should be soft but it should still have a bite to it). Drain and set aside.
Pat dry shrimp with paper towels, toss with Cajun seasoning (mine already contains salt so I'm not adding any).
Heat oil and butter in a large frying pan over medium-high heat. Cook shrimp in two batches, until browned on both sides and cooked through. Make sure the shrimp is not overcrowded. Place the shrimp in a pan in a clockwise pattern. When it's browned start to flip it one at a time starting with the first shrimp you have put in the pan going also clockwise (use kitchen tongs or two forks). Transfer the shrimp to a plate.
Reduce the heat to low, add minced garlic (add some more butter if the pan is too dry). Cook it for 30 seconds.
Add flour, cook it, whisking, for a minute.
Add white wine and lemon juice. Cook it, whisking, until the wine is almost evaporated.
Add cream, milk, and broth. Cook for 1-2 minutes until well combined. Make sure to scrape all the browned bits at the bottom of the pot.
Gradually add cheese, whisking after each addition and waiting for the cheese to melt.
Cook the sauce for 1-2 minutes, until thickened. It should be rather runny at this point - it will thicken considerably while cooling.
When all the cheese is melted and the sauce is smooth, season it with salt and pepper and toss with cooked pasta.
Arrange the pasta with sauce on plates, top with cooked shrimp. Squeeze a small amount of lemon juice over shrimp and sprinkle with chopped parsley.