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1
Grease the bottom of a large bowl with olive oil.
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2
Pour the warm water into the bowl of a stand mixer fitted with the dough hook.
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3
Evenly sprinkle the yeast and sugar over the water.
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4
Mix at low speed until combined, 30 seconds.
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5
Add the flour, rosemary, 1/2 cup of the olive oil and 4 teaspoons of salt and mix at medium speed until a dough forms, about 5 minutes; it will be a little sticky.
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6
Form the dough into a ball and transfer to the greased bowl.
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7
Cover tightly with plastic wrap and let stand at room temperature until it doubles in bulk, about 2 hours.
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8
Punch the dough down in the bowl and form it into a loose ball.
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9
Cover with plastic wrap and let stand at room temperature for 1 hour.
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10
Meanwhile, in a small, heat-proof bowl, cover the figs with boiling water.
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11
Let stand until softened, 1 hour.
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12
Drain the figs and slice them 1/4 inch thick.
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13
Lightly grease a 9-by-13-inch rimmed baking sheet.
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14
Transfer the dough to the prepared pan and, using your fingertips, press it out to fill the pan.
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15
Cover with plastic wrap and let rise at room temperature for 30 minutes.
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16
Preheat the oven to 375.
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17
Arrange the fig slices all over the dough; gently press them in.
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18
Drizzle with 2 tablespoons of the olive oil and season with salt and pepper.
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19
Sprinkle the cheese over the top.
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20
Bake for 25 to 30 minutes, rotating the pan halfway through, until golden and firm.
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21
Let cool slightly on a rack.
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22
Drizzle with the remaining 2 tablespoons of olive oil and serve warm or at room temperature.
