Preheat the oven to 375ºF / 190ºC and brush a muffin tin with olive oil.
Place one sheet of the phyllo dough on a board and brush or spray with olive oil. Keep the remaining sheets covered with a damp cloth so they don’t dry out.
Repeat the process, layering and brushing the dough with olive oil.
Once you’ve completed the layers, cut the stack into 6 squares, then press each square into the prepared muffin tin.
Bake for 6–8 minutes until golden and crispy.
In the meantime, make the filling: whisk the olive oil, vinegar, and oregano in a bowl to combine. Add the tomatoes, olives, feta, and cucumber, tossing everything together.
Once the phyllo cups have cooled, fill them with the feta and olive mixture, and sprinkle with chopped chives before serving.