Freeze the cheese for 15 minutes to make it easier to slice and help it keep its shape when fried.

Crack the egg into a shallow bowl, add 1 tablespoon of water, and whisk until combined. Set up two more shallow bowls: one with flour and another with breadcrumbs. Set a plate with the za?atar to the side.

Remove the cheese from the freezer, slice it into 1/2-inch discs.

Dip each goat cheese disc into the egg mixture, then coat with flour, and finally the breadcrumbs. Shake off any excess crumbs and set aside on a large cutting board or sheet tray.

Heat about 2 tablespoons of olive oil in a large nonstick skillet over medium-high heat. Once shimmering, add goat cheese discs without crowding the pan. Cook until golden brown, about 30 seconds per side.

Remove from heat and drain on a plate lined with paper towels.

While the cheese is still hot, roll each disc in the plate of za?atar to coat.

Transfer to a serving plate and serve immediately.