The Grilled Cheese Aspiration is generally considered undesirable, but confers some minor, unique benefits.It is not available in any of the Aspiration menus (which pop up when a Sim is created, grows into a teen or finishes junior year at university). However, it can be gained using a cheat code or when the ReNuYuSenso Orb fails.
It has been suggested that the Aspiration was inspired by the frequency with which some Sims made the sandwiches autonomously in the original Sims 2.
Hints
Grilled Cheese Sims have very few high-scoring Wants, but can satisfy small Wants more frequently.
If your sim has the Grilled Cheese Aspiration, you can take advantage of their constant want of eating grilled cheese sandwiches. First, prepare a grilled cheese sandwich (or serve a plate of them for even more aspiration) then take one to the table and eat it. When you receive your 500 aspiration points, cancel eating it, then proceed to click on the same sandwich again, therefore getting 500 more aspiration points. You can repeat this numerous times and you can boost up your aspiration level quite fast.
When the "Serve Grilled Cheese Sandwich" want is in a Want Box (which it almost always is, particularly if you control a Sim who's either in college or a college graduate, since they have five and six Want Boxes, respectively), simply have another Sim eat the sandwich your Sim has prepared, and you'll net 1,500 Aspiration points. In a large family or dormitory this allows you to rack up Aspiration points at an insane rate, and your Sim will be in Platinum Mood in no time.
This will allow you to buy more Aspiration Rewards, and when you're ready to change Aspirations you should be able to use the ReNuYuSensoOrb successfully.