Yes it is absolutely possible!
Soft-boiled eggs are delicious. I make them all the time, love it especially on ramen:
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The trick is to boil the egg in a rolling boil for 5 or 6 minutes depending on the size of the egg, then dumping them in cold water to stop them from cooking further. This product might help too.
You have to be a little bit more careful thenthan with hard-boiled eggs when peeling, but it really isn't very hard to do!
I then dip the meat from my ramen in the egg yolks, and later break the white in pieces and eat it with the noodles. Yum!