Preheat oven to 250 degrees F. Make slow-roasted tomatoes by slicing tomatoes in half lengthwise. Place cut side up on baking sheet; sprinkle with salt and pepper. Place in oven and roast for 2 1/2 to 3 hours. (Tomatoes may be made ahead and stored in refrigerator for up to three days.).
In large skillet, melt olive oil and butter over medium high heat. Season chicken with salt and pepper. Add chicken to skillet and sauté, turning, until browned, about 3 minutes per side. Remove chicken from pan, cover and reserve.
To same skillet used to cook chicken, add one tablespoon olive oil. Add diced onion and sauté over low heat until soft, about 10 minutes. Add prosciutto and sauté for 30 seconds. Add slow-roasted tomatoes and break up with back of wooden spoon. Heat through for 30 seconds. Add cream; remove sauce from heat.
Cook pasta according to package directions. When pasta is almost done, reheat sauce over low heat. Add peas and sage to sauce; stir to heat well. When pasta is cooked, drain but do not rinse. Add pasta to sauce in skillet and toss well to combine. Add cheese and parsley; toss again. Place on serving platter and top with chicken.