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1
Preheat the broiler. In a small skillet, melt the butter in the olive oil over moderate heat. Add half of the shallots and garlic and cook, stirring often, until softened and fragrant, 2 to 3 minutes. Season with a pinch of salt and pepper. Scrape the mixture into a small bowl and let cool.
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2
Loosen the skin from the chicken breasts without detaching it completely. Place a teaspoon of the cooked shallot and garlic mixture under the skin of each breast half and spread it over the meat. Top the mixture with a folded piece of prosciutto and 3 basil leaves. Smooth the chicken skin over the fillings and season lightly with salt and pepper.
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3
Set the chicken in a medium roasting pan, skin side up. Broil for 5 minutes. Turn and broil for 5 minutes more, then turn again and broil for about 5 minutes longer, or until nicely crisped on top; take care not to burn the skin. Turn the oven temperature to 350u00b0 and bake the chicken for about 20 minutes, or until the juices run clear when the meat is pierced. Transfer the chicken to a plate and keep warm.
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4
Pour the juices from the roasting pan into a small bowl; spoon off the fat and reserve the brown drippings. Place the roasting pan over moderate heat. Add the remaining chopped shallot and garlic and stir until softened and golden, about 2 minutes. Pour in the wine and bring to a boil. When the wine is nearly evaporated, pour in the chicken stock and heavy cream. Bring to a boil and simmer, stirring occasionally, until reduced to 1/2 cup, about 4 minutes. Stir in the reserved drippings and the minced basil and season with salt and pepper.
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5
Place a stuffed breast half on each of 4 dinner plates. Spoon the sauce over or around the chicken and serve.
