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If using stand mixer, combine flour, salt, egg, olive tapenade, butter, water and proofed yeast in bowl. Use dough attachment, set to low speed, to combine until dough forms. (This step takes around 6-8 minutes.) Dough texture should be soft, but not sticky. Note: If you are not using a stand mixer, knead by hand for 8-10 minutes.
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Transfer dough to greased bowl. Lift dough, turn it upside down and return to bowl to grease both sides. Cover mixing bowl with plastic wrap and let dough rest for about 2 hours on countertop or inside an oven with the light on.
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Once dough has doubled in volume, punch to deflate. Transfer to lightly floured surface and knead for 2-3 minutes. Divide dough into 12 pieces (eyeball it). Shape each piece into smooth, round rolls.
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Line a 9x13-in. pan with parchment paper or spray with cooking spray.
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Arrange rolls an inch apart and cover with plastic wrap. Set aside for 1 hour. The rolls should have doubled and filled the pan.