Season prawns with salt, pepper, paprika and oregano. Drizzle with about 1 tablespoon EVOO and toss to coat. Wrap a slice of ham around each prawn.
Heat a skillet over medium-high heat with remaining 2 tablespoons EVOO. Add ham-wrapped prawns to the hot pan in a single layer. Sear until golden brown and cooked through, about 3 minutes per side.
Serve the prawns with the lemon wedges alongside.