I think it's unrealistic to expect a 2 year old to be able to play by themselves for a long time. Some might, but not all.
We tried the "cry it out" technique tonight but we know it'll take
more than one instance to break this behavior.
Is there a better approach than "cry it out" to break our son of this
Wanting to be with his parents ...
Your son wants interaction because you're the two people in the world that he cares most about. It is often boring playing on his own, and he isn't getting as much positive feedback by himself — he doesn't know if the thing he's done is worthwhile.
There is no silver bullet to address anything with children because every child is different, and every child ...
Toddlers are very social. We also had difficulties cooking while the children wanted to be with us. Having lots of toys and books helped somewhat. Another big help was a toy kitchen with a toy stove, sink and countertop. This, plus a set of toy plastic dishes and metal cookware and a set of plastic fruits and veggies occupied our children while we cooked.
What I'm doing is I keep doing whatever I want, but put the boy near me. And then I speak and explain in loud what I'm doing.
"Opening eggs, mixing, boiling..." Then, he is with me. Learn to speak, to listen, I'm more focused on what I'm doing, and on him.
Anecdotal: we newer got our child to play independently when we are around but grandma did. She would give him a wooden train set to play with. Then she would play with him for a while and show him how to and then tell him she would go and cook. The cooking happened around the corner in the same room.
I think it was a combination of 1) the interesting toy ...