Roast the red peppers until blackened. Place the peppers in a bowl & cover with wrap to generate steam for approximately 5 to 10 minutes. Remove the blackened skin and seeds. Cut each red pepper into thirds.
Cut the chicken in half horizontally almost but not all the way through. Open the chicken like a book and season with salt and pepper.
Place a slice of roasted red pepper onto one side of the opened chicken breast. Top each with 2 basil leaves. Sprinkle with cheese. Fold the other side of the chicken over creating a bundle. Secure the chicken bundle with three pieces of string.
In a large non-stick pan, heat half of the olive oil over medium heat. Add the chicken and cover. Cook for approximately 7 minutes per side or until no longer pink inside.
Remove to plate and remove strings.
Add the remaining oil to pan, and cook the garlic and shallots until softened.
Stir in wine and boil for 3 minutes.
Stir in whipping cream. Season with salt and pepper. Simmer for 5 minutes or until thickened enough to coat the back of a spoon.
Return chicken to the pan, turn the chicken to coat while reheating.
Remove the chicken to individual plates. Spoon the white cream sauce over the chicken and garnish with fresh juliened basil.