The word desayunabas is the imperfect form of desayunar in the second person singular. There are other translations for this conjugation.
See the full desayunar conjugation

desayunar

¿Sabe usted que sus hijos me la pidieron otro día si desayunabas todavía vive con nosotros?
Do you know that your sons asked me the other day if you acctually still live with us?
Pensé que no desayunabas.
Thought you didn't do breakfasts?
Creí que no desayunabas.
I thought you didn't do breakfast?
Lo vi en ti cuando desayunabas.
Yes. I could tell at breakfast.
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