Can bearded dragons eat cooked food? 

I guess it all depends on what we are defining as cooked food, a bearded dragons diet should consist of vegetation and live insects. There are some prepared "cooked" bearded dragon diets that come in the form of dried pellets, tinned fruit and vegetables and even cooked crickets but rarely do the dragons find them palatable.

If we are saying cooked food as in what us humans eat? then there are some that are possible but the need should never need arise, first of all things like peanut butter, cooked desserts, pastas, pizza, ready meals etc etc are all big NO.

If you were unable to source any protein for your dragon as in no insects were available or any defrost rodents then some good quality chicken or lean beef could be finely diced and cooked, your dragon may not eat it but being an omnivore it wouldn't be the end of the world to feed it to your dragon but doing it as a permanent part of the diet or anything other than an emergency is strongly not advised.

Lastly cooked food could mean tinned dog or cat foods, these are formulated to provide for the needs of cats and dogs, do not feed them to your pet dragon as part of their diet. If your dragon is free roaming one day and you catch him having a nibble from the dogs bowl, don't panic being an omnivore its usual for them to scavenge from sources of protein but don't think that he likes it so it should be part of his diet.

Just to reiterate your Bearded Dragons diet should be made up of fresh vegetable matter usually leafy green salads and live insects. Additional sources of protein can be offered in the form of defrosted pinkie mice as a very occasional treat.  Anything other than this mix doesn't really need to be considered.