Preheat the oven to 425 degrees F.
Snip the hard stems off the figs and cut the figs in half lengthwise through the stem. With a small sharp knife, cut the prosciutto lengthwise into inch-wide strips. Wrap a strip of prosciutto around the center of each fig half, with the ends overlapping. Brush with olive oil and arrange cut-side up on a sheet pan.
Roast the figs for 10 minutes, until the prosciutto is a little crisp and the figs are warmed through. Serve warm.
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