Heat a large flat-bottomed skillet over medium high heat. When hot, add olive oil. When oil is hot, add onion. Saute approximately 5 minutes, until beginning to brown. Add cauliflower, and saute an additional 10 minutes. Add eggplant, adding more oil to skillet if necessary. Continue to stir and saute an additional 10 minutes or so, until eggplant and cauliflower are golden and cauliflower is tender. Stir in garlic, and turn off heat. Stir in grated carrot and most of the basil, saving approximately 2 tablespoons for garnish.