Remove skin from chicken thighs; place in a slow cooker with tomatoes, chicken broth, mushrooms, and thyme.
Cover slow cooker and cook on Low for 8 hours.
Fill a large pot with lightly salted water and bring to a rolling boil. Stir in penne and return to a boil. Cook pasta uncovered, stirring occasionally, until tender yet firm to the bite, 9 to 11 minutes. Drain.
Combine Parmesan cheese and Romano cheese together in a bowl. Scoop 1 cup of tomato mixture from slow cooker and stir in cornstarch. Pour cornstarch mixture back into slow cooker and stir well to combine. Cover and cook for 10 minutes, stirring occasionally. Turn slow cooker off. Stir in cooked penne and top with cheese mixture.