How can two brown-eyed parents produce a blue-eyed offspring?

If both parents are heterozygous (xX) and the blue allele (x) is recessive to the dominant brown allele (X), the offpring has a 1/4 chance of getting homozygous recessive alleles (xx).

If one or more of the parents are homozygous dominant (XX), the genes could be mutated (insertion, deletion, substitution) before it is passed on to the offspring, preventing it from from being expressed, producing a recessive phenotype in the offspring and potentially a new allele of the gene.