In a stand mixer fitted with the dough hook, combine the flour, yeast, and salt. Mix on low speed to combine.
Add the lukewarm water, sugar, eggs, and the melted butter. Knead on medium-low speed until you have a sticky dough that clings to the bottom of the bowl, 5 to 7 minutes. The dough will be sticky.
Dust your hands generously with flour, then scrape the dough out onto a lightly floured work surface. Dust the top of the dough lightly with flour and knead briefly into a soft, smooth ball. Lightly grease a large bowl with oil or non-stick cooking spray. Place the dough in the bowl, flip it over once so the top is lightly oiled, and then cover the bowl with plastic wrap. Allow the dough to rise in a warm, draft-free spot until it's puffy and doubled in size, 2 to 3 hours.
As the dough rises, prepare the filling in the next step and grease a 9×5 inch loaf pan.
Combine the Za’atar and olive oil in small bowl mix until combined. Set aside.
Punch down the dough to release the air and then place on a lightly floured work surface. Divide it into 12 equal pieces. Using lightly floured hands, flatten each into a circle that’s about 4 inches in diameter. The circle doesn’t have to be perfectly round. Spread 1-2 teaspoons of filling mixture onto each. Fold circles in half and line in prepared baking pan, round side up. Cover pan with plastic wrap and let rise until dough does not spring back when pressed with a finger, 30-45 minutes.
Preheat oven to 350℉. Brush raised bread with egg wash.
Bake loaf until golden, 25 to 30 minutes. Let cool 10 minutes before turning out of pan; serve.