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To make Dough: Stir yeast into 1/4 cup warm (105115F) water until dissolved.
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Let stand 10 minutes.
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Stir 3/4 cup flour, sugar, and 1/2 cup warm water into yeast.
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Cover, and let stand 30 to 45 minutes, or until very bubbly and fragrant.
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5
Combine remaining 21/4 cups flour and salt in bowl of food processor, stand mixer, or regular bowl.
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(Reserve 1/3 cup flour if kneading by hand.)
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7
Stir oil and 1/2 cup warm water into yeast mixture.
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Stir yeast mixture into flour mixture.
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(If using food processor, add liquids through feeding tube with processor running.
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If using stand mixer with dough hook, add liquids in steady stream with mixer on low speed.)
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Follow kneading below.
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Place Dough in lightly oiled bowl.
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13
Cover, and let rise in warm place 45 minutes to 1 hour, or until doubled in size.
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14
Lightly oil 15- x 10-inch jelly-roll pan or rimmed baking sheet.
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15
Gently stretch or press Dough into pan as evenly as possible with fingers; brush with oil.
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Make indentations with fingertips all over Dough.
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Cover, and set aside 30 minutes, or until doubled in size.
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18
To make Topping: Preheat oven to 425F.
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19
Heat 1 Tbs.
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oil in large skillet over medium heat.
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Add onion, and saute 3 to 4 minutes, or until soft.
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Stir in 11/2 tsp.
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rosemary, and season with salt and pepper, if desired.
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Reduce heat to medium-low, and cook 4 minutes more, or until tender and translucent.
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Transfer to plate.
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Add remaining 1 Tbs.
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oil to same skillet, and saute apples and remaining 11/2 tsp.
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rosemary 6 to 8 minutes, or until softened.
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Stir onion and sugar into apple mixture.
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Sprinkle apple-onion mixture evenly over Dough.
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Bake in upper one-third of oven 20 minutes, or until edges are golden and bottom of focaccia is golden brown.