Combine oregano, salt and black pepper in a small bowl. Sprinkle over halved chicken breasts on both sides.
Heat skillet with vegetable oil under medium high heat. Once oil is hot, sear chicken breast on one side until slightly brown (about 1-2 minutes), then flip and sear the other side (another 1 minute or so). Remove chicken once the other side is lightly browned and set aside. The goal is to sear seasonings into the surface of the chicken - chicken does not need to be fully cooked. Cook in two batches if skillet is not big enough.
Add crushed tomatoes, tomato paste, red wine, garlic, and sugar to slow cooker. Mix to combine.
Add slices of chicken breast to slow cooker, and nestle them into the sauce. Then add onions, bell pepper, mushrooms, and then top with a very sprigs of fresh thyme. Use a spoon to submerge the ingredients into the sauce as much as possible (okay if not fully submerged).
Cook on high for 3 hours.
Remove lid and add salt to taste. Salt will open up the flavors of the sauce.
Discard bay leaf, thyme and garlic pieces. Serve chicken with (lots of) sauce over a bed of pasta. Enjoy!