In a skillet, heat olive oil on medium heat. Place a slice of bread in the middle of the skillet. Press down and slide bread around so olive oil gets on as much of the bread as possible.
Top bread with cheese and tomato. Cover with 2nd slice of bread. Cook until bottom slice begins to brown. Lift up sandwich with a spatula. Add the other teaspoon of oil and oregano to the skillet. Flip sandwich and grill the 2nd side until bread is a golden brown. Serve while warm.