For Pancakes: Preheat oven to 400°F. Pierce eggplant all over with fork. Place 2 Tbsp oil on cookie sheet. Add eggplant and turn to coat. Bake until very tender, turning once, about 55 minutes. Cut in half lengthwise and let cool.
Using spoon, scrape flesh from eggplant into sieve. Drain 1 hour, pressing occasionally on eggplant with spoon. Transfer to bowl. Mash with fork.
Heat 1 Tbsp oil in heavy small skillet over low heat. Add onion and garlic and saute until tender, about 6 minutes. Add to eggplant. Mix in flour. Mix in egg. Season with salt and pepper. (Can be made 4 hours ahead. Cover; chill.)
For Lamb: Preheat oven to 500°F. Brush lamb with some of Basil Oil. Season with salt and pepper. Heat 2 tablespoons olive oil in large oven proof skillet over medium-high heat. Add lamb, meat side down, and brown 8 minutes. Turn and brown 2 minutes. Transfer to oven; roast about 10 minutes for rare. Place on work surface. Let rest 10 minutes.
Meanwhile, heat 1 Tbsp olive oil in large non stick skillet over medium heat. Add eggplant, using 2 Tbspfuls for each pancake, spacing evenly. Cook until golden, about 5 minutes per side. Transfer to plates. Repeat with 1 Tbsp oil and remaining eggplant. Carve lamb into ribs. Place on plates with pancakes. Drizzle with Basil Oil.
Basil Oil: Remove basil stems from leaves. Place 5 leaves and oil in blender. Process to coarse puree. Let stand 1 hour. Strain.