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1
Combine warm milk, yeast, and sugar in the bowl of a stand mixer fitted with the paddle attachment. Let stand until mixture is foamy, 5 to 10 minutes.
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2
Beat milk mixture on low speed. Add 1 cup flour, beating just until combined. Add melted butter, 2 tablespoons olive oil, and 1/2 cup flour; beat until combined. Beat in eggs. Add remaining 1 3/4 cups flour and salt. Beat until a soft, sticky dough forms.
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3
Spray a large bowl with cooking spray; add dough. Cover loosely and let rise until doubled in size, about 1 hour.
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4
Preheat oven to 350 degrees F (175 degrees C). Grease a 12-cup muffin tin with cooking spray.
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5
Punch dough down gently. Pinch off 36 small pieces of dough and roll into balls.
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6
Whisk 6 tablespoons za'atar and 1/3 cup olive oil together in a bowl. Immerse dough balls in oil mixture to coat all sides. Arrange 3 dough balls in each muffin cup. Sprinkle remaining 2 tablespoons za'atar over dough.
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7
Cover muffin tin loosely with greased plastic wrap. Let rise until dough balls puff up over the rim of the tin, about 25 minutes.
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8
Bake in the preheated oven until puffed up and golden, about 25 minutes. Cool for 5 minutes in the pan. Lift out of the pan and cool briefly on a wire rack, about 5 minutes more.
