In a bowl whisk up eggs, a pinch of salt, and sage.
Heat a 12-inch nonstick skillet over moderate heat and use a very thin spatula or fish spatula to manipulate the eggs. Swirl in butter to coat the pan and when it foams let it begin to brown. Add eggs and let them settle, then gently lift pan a bit and begin swirling the eggs to edges of bottom of pan, forming a thin omelet about 10 inches wide. When the eggs begin to dry on top and steam, a few bubbles will form. Remove pan from heat and top with prosciutto, layering it evenly down the center and covering the surface. Place arugula in a small bowl and add a few curls of Parmigiano-Reggiano, then dress with lemon juice and EVOO and season with salt. Top ham with greens and figs, again working down the center of the crepe. Fold in sides of crepe, like swaddling a doll. Carefully transfer to plate.