Cut chicken breasts in half, width-wise, to make four thin chicken breasts. Season chicken with salt and pepper. Cook over medium heat with some oil, until it's done. Take out of the pan and set aside to cool.
Preheat the oven to 350 and get a rimmed baking sheet.
Wash portobello caps and gently cut out the stems. Make sure not to cut a hole in the bottom and don't make the bottom too thin.
Rub each mushroom cap with oil on the outside and set them in a baking sheet.
Season inside of each mushroom with salt and pepper. Spread about a tablespoon of pasta sauce in each mushroom cap.
Once the chicken is cooled enough to handle, dice it small and add it to a mixing bowl.
Add leftover pasta sauce (about 3/4 cup) to the chicken. Add 3/4 cup shredded Mozzarella cheese, diced basil leaves, thyme, salt, and pepper. Mix well.
Divide the chicken mixture among the portobello mushroom caps.
Divide 1/2 cup of shredded Mozzarella cheese over the tops of the chicken mixture.
Bake for 20-25 minutes, depending on thickness of portobello mushrooms.
Grate some Parmesan cheese over the top of the cooked stuffed mushrooms.