One option is to line your strainer with cheesecloth, which will keep just about anything from getting through. Since you're only putting pasta, water, and broccoli through it, uou can rinse and re-use the cheesecloth so it's cost effective.
I buy my cheesecloth in bulk at fabric stores, as it's significantly cheaper there than any food-related store I've ever been to.
Simply put, you have to stir them the first three/four minutes of cooking. Be sure to boil them in enough water (at least 1 liter per 100 grams). In addition to that be sure to buy some good quality pasta. From my knowledge pasta tends to stick when the wheat used is of poor quality. A good pasta should not be transparent when seen in direct sunlight, but it should be of a nice pale yellow color and opaque. Good Italian pasta brands that you can find outside of Italy are De Cecco (which I fear might be quite expensive, and probably not so easy to find), or Barilla (easier to find). Both of them has cooking instructions printed on the package. You might want to cook them for 2-3 minutes less than what's printed, then eventually cook them the remaining couple of minutes together with your sauce.
Best Answer
Honestly, you either eat it fresh, or accept it will congeal.
There are 2 factors going on,
the pasts will keep absorbing water until there's almost none left
the cheese will set as it cools.
The upside is 'yesterday's mac cheese' is great in & of itself.
Your only 'fix' is make it wetter or eat it sooner.