Preheat a small nonstick fry pan over medium-low heat.
Assemble the sandwich by placing sliced cheese between the two slices of whole wheat bread so the cheese covers the bread.
Drizzle 1 teaspoon of the olive oil into the warm pan and tilt the pan to spread it evenly.
Place the sandwich in the pan, cover with a lid, and cook until the bottom is golden, about 2 minutes.
Lift the sandwich with a spatula, add the remaining 1 teaspoon of olive oil to the pan, then flip the sandwich and cook the other side until golden, about 1–2 minutes more.
Remove from the pan and serve immediately.