Bring a pot of salted water to a boil and add pasta. At the same time, preheat a wok or large frying pan over medium-high heat.
Put frozen precooked shrimp in a bowl and cover with cool but slightly warm water to thaw.
Peel and roughly chop garlic, and chop broccoli into small bite-size pieces. The stem is perfectly good to eat too! Just peel it and slice it up.
As soon as the wok or frying pan is hot, add 2 tablespoons of olive oil and 1 tablespoon of cajun seasoning. Fry for a few seconds but don't let it burn.
Add broccoli and start to stir fry it. You'll have to stir it around quite a bit to keep it from burning. Adjust heat slightly if it seems too high. You want to cook it fast but not burn it. I cooked mine for around 4 minutes, but that could vary based on the heat of your burner, the size of your broccoli florets and the pan you're using (my wok is cast iron and conducts heat amazingly well). The broccoli will turn a lovely, bright green.
While the broccoli is cooking, the pasta should be ready (mine took around 9 minutes to al dente). Before you drain it, use a mug or measuring cup to take out some nice, starchy pasta water. Then drain the pasta.
Add the chopped garlic and 1 more tablespoon of olive oil, and stir it around to cook for about a minute.
Add thawed shrimp (drain the water first), 1 more tablespoon of olive oil, 1 more tablespoon of cajun seasoning (try a taste of broccoli first, to make sure it's not too spicy - cajun seasoning can vary in heat) and 1/4 cup pasta water. Toss it all together to make sure it's well-mixed and shrimp are heated through until piping hot.
Taste a noodle to see if it needs salt (if it doesn't taste bright or the flavour seems dull, it needs salt. Unless you're on a special low-salt diet, don't skimp on salt in this, or any other recipe. It brings the flavour). I added 1/2 teaspoon of salt.
Enjoy! :)