Dredge the eggplant in the flour and bat against hand to remove excess. Dip in the egg, turning to completely coat. Dip in the bread crumbs, coating completely.
In a 12 to 14-inch saute pan, heat the olive oil until just smoking. Add the butter and heat until it foams and subsides. Cook the eggplant in the pan, turning so that both sides are uniformly dark golden brown. Remove from the pan, season with salt and pepper and drain briefly on a plate lined with paper towels. Drizzle with the balsamic vinegar and serve immediately with Tomato Bruschette.
Combine tomatoes, basil, olive oil and garlic. Season with salt and pepper. Serve on top of grilled bread.