B = brown, which is dominant
b = blue, which is recessive

BB is brown eyes
Bb is brown eyes but still carrying the blue eyed trait
bb is blue eyes

If one parent is BB and the other parent is bb, all offspring will be Bb and have brown eyes

If there is a Bb parent and a bb parent, it is 50/50 whether their offspring will have brown or blue eyes

If both parents are Bb, there is a 1 out of 4 chance the baby will have blue eyes

So, when trying to determine the odds of two brown eyed parents having a blue eyed child, we need to be able to figure out if the parents are BB brown or Bb brown. The best way to figure that out would be to look at a family tree. I don't know the actual prevailing rates for BB vs Bb otherwise, but lets just assume its 50/50. In that case, the odds of both brown eyed parents being Bb is only 1 in 4

So the odds of two brown eyed parents having a blue eyed kid is roughly 1 in 16