Season both sides of chicken with salt and pepper.
In a large saute pan, heat butter and olive oil over medium until butter is melted. Add chicken and saute for about 2-3 minutes per side until browned. Remove from pan to plate and reserve.
Add chopped mushrooms and saute, stirring occasionally. After about two minutes, add garlic and shallots. Continue to cook for another two minutes. Add wine to pan, bring to a boil and reduce until almost gone, about 4 minutes. Add tomatoes and juice, continue to boil until slightly reduced, another 3 or 4 minutes. Add 2 tablespoons basil and rosemary. Turn heat to low.
Make the grits by bringing the stock, cream, water, garlic, and butter to a boil. Slowly whisk the grits into the liquid. Bring back to a boil, reduce heat and cook, stirring occasionally for 15-20 minutes or until grits are thickened. Turn heat to low and stir occasionally while finishing chicken.
Add chicken and any accumulated juice back to pan with mushroom tomato sauce. Turn heat to medium and cook chicken for about 5 minutes until chicken is heated through.
Divide grits into soup bowls, place two pieces of chicken on top of each bowl, spoons mushroom tomato sauce on top. Garnish with additional 2 tablespoons basil and serve.