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 in half 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.