* Peel and cook sliced carrots until soft. Drain, and place carrot slices in a 350 degree oven for 10 minutes. Puree in a mixer. The carrot puree should be thick.
Preheat the oven to 375 degrees. Brush the interior of a 6-cup soufflé mold with the softened butter.
In a heavy saucepan heat the olive oil. Add the onions and garlic. Cook briefly while stirring, until onions are wilted. Stir in the flour and cornstarch. Add the milk. Cook while whisking until sauce becomes thick.
Tranfer the bubbly sauce to a large mixing bowl. Season with salt and pepper and mix in chopped basil.
Mix egg yolks, and carrot puree into the thick cream sauce. This mixture can be prepared 2 hours ahead.
Using an electric beater, whip the egg whites and cream of tartar until stiff and glossy. Do not overbeat. Gently fold into cream sauce mixture. Pour and scrape the mixture into the prepared soufflé mold.
Place on a baking sheet. Cook for 20 to 30 minutes. Serve at once.