The cleaned shrimp can be dried with a paper towel. Sprinkle 1/2 tsp cajun seasoning on top.
Cook the linguine as per the instructions on the pack and let cool.
Heat a large pan over medium heat
Add the oil, butter
Place the shrimp in an even layer, then add the minced ginger. After 2 minutes turn the flame on and continue cooking for 1-2 more minutes, or until it is pink.
Add the half-and-half and parmigiano Reggiano to the pan
Bring to a boil and whisk for 2 minutes.
Turn heat off
Add the pasta
Add the chopped tomato and 1/2 tsp Cajun seasoning.
Add the lemon juice. This step can be skipped as adding lemon juice and dairy can cause problems. But if you leave the heat off, there is a greater chance that it won't happen.
Stir it to combine. As it cools, it will continue thickening.
You can add more half and half if the sauce seems too thick.
Serve