"The woman has a honey cake" should be correct. Nobody says "Cake with honey" unless they are two separate things.
That actually isn't correct because the sentence says cake with honey. With is a word that has been placed within the sentence on purpose because they ate two seperate things.
Mia, I disagree because all their other examples such as chocolate cake written as "cake with chocolate." Maybe a native speaker can describe the difference.
Diferenta este ca nu poti construi tort din miere ci doar poti pune miere in compozitia cremei ...nu stiu acum daca in blatul tortului poti pune miere...un sef bucatar stie asta!