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1
Bring 1 cup water, Port, figs, and rosemary to boil in small saucepan.
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2
Reduce heat to medium-low; simmer until mixture is reduced to generous 1 1/4 cups, stirring occasionally, about 20 minutes.
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3
Cool slightly.
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4
Puree in processor until smooth.
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5
do ahead Fig jam can be made 3 days ahead.
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6
Cover and chill.
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7
Preheat oven to 400F.
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8
Place onion rounds on rimmed baking sheet.
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9
Dot with butter.
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10
Sprinkle with salt and pepper.
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11
Roast until tender and golden, about 45 minutes.
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12
DO AHEAD: Can be made 2 hours ahead.
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13
Let stand at room temperature.
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14
Spread about 1 1/2 tablespoons fig jam on bottom of each ciabatta roll.
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15
Top with onions, prosciutto, and cheese.
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16
Place roll top on each.
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17
DO AHEAD: Can be made 2 hours ahead.
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18
Let stand at room temperature.
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19
Cook panini in panini press according to manufacturer's instructions.
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20
Alternatively, heat heavy large skillet over medium heat.
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21
Working in batches, place panini in skillet.
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22
Place large cast-iron or other heavy skillet atop panini.
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23
Fill skillet with bricks or large cans to weigh down.
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24
Cook until bottoms of rolls are golden, about 4 minutes.
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25
Remove top skillet and turn panini over, then place skillet atop panini.
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26
Cook until golden and cheese melts, about 4 minutes longer.
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27
Cut in half and serve.
