Cut the kefalotyri or graviera cheese into 4 slices, each about 1.5 cm / 0.6 inch thick. Pat both sides dry with a paper towel.
Set up two shallow dishes with the flour and a small bowl with the water. Dredge each cheese slice in flour, dip quickly into the water without soaking it, then dredge in flour again, pressing gently so the coating sticks. Shake off the extra flour.
Heat 2 tbsp of the olive oil in a 10-inch (25 cm) nonstick skillet over medium heat for about 2 minutes, until it shimmers and looks wavy.
Add 2 cheese slices to the skillet, leaving space between them. Fry for 1.5 to 2 minutes per side, until the crust is deep golden brown and the cheese is soft in the middle but still holding its shape.
Lift the cheese out with a fish spatula and set it on a plate. Wipe out any loose bits of burnt flour from the pan, add the remaining 2 tbsp olive oil, and fry the second batch the same way.
Squeeze fresh lemon juice over the hot cheese as soon as it comes out of the pan.
Sprinkle with dried oregano and a pinch of black pepper. Serve right away, with the rest of the lemon cut into wedges on the side.