Preheat oven to 400°F.
Add the breadcrumbs, olives, parmesan cheese, capers, parsley, 2 tablespoons of the olive oil and 1/4 teaspoon of the salt into a medium bowl and combine.
Lay the turkey breasts on a flat work surface cut side up. Season the insides with 1 teaspoon of salt. Place three slices of cheese down the center of each breast. Sprinkle the breadcrumb mixture evenly over both breasts.
Begin with the skinless end of the breast, use clean hands and roll the turkey breast up tightly. Tie the rolled up breast in three places with butcher string. Season the outsides of both breasts with the rest of the salt.
Heat a medium oven proof pan over medium high heat. Add the remaining olive oil to the pan and heat another 30 seconds. Place the turkey breasts skin side down to the pan and cook, undisturbed, until there is a golden brown braise appears. This will take 4 to 5 minutes. Flip the breasts carefully, and cook an additional 3 minutes on the other side. Being careful not to lose stuffing, move the breasts to a plate.
To the pan, add the garlic and cook for 2 minutes. Drop the heat to low. Deglaze the pan with white wine and stir up the brown bits from the bottom of the pan using a wooden spoon. Bring the wine to a simmer. Stir in the tomato puree. Lay the basil across the top of the sauce. Place the breasts back in the pan and cover with lid.
Place in the oven and cook until the internal temperature reaches 145°F. This will take about 30 minutes. Uncover and cook another 15 minutes or until internal temperature reaches 160°F.
Remove from the oven, place lid back on and rest for 15 minutes before serving.
Slice, top with warm tomato gravy. Enjoy!